VJX  }_} 


UC-NRLF 


TABLES 


OF 


HARMONIA 


University  of  California. 


TABLES 


OF 


HARMONIA 


9 


BY 


E.    SCHUBERT. 


COMPUTED  FOR  THE 


AMERICAN  EPHEMERIS  AND  NAUTICAL  ALMANAC, 


*&-    OP  THB***^ 

riU-7.EBSIT7] 


BUREAU  OF  NAVIGATION, 

WASHINGTON. 

1869. 


\v 


- 


INTRODUCTION, 


A  COMPLETE  list  of  the  general  perturbations  of  Harmonia  by  Jupiter  and  the  determination  of  the 
•£*•  elements  by  means  of  them  having  been  published  in  Vol.  LXVI  of  the  "  Astr.  Nachrichten,"  it  is  only 
necessary  to  repeat  here  the  retained  terms  of  the  perturbations  in  the  contracted  form  and  the  elements 
upon  which  the  Tables  have  been  constructed. 

In  these  M  and  M'  are  the  mean  anomalies  of  Harmonia  and  Jupiter  respectively. 
Denoting  the  arguments  as  follows : — 


1  =  -      M' 

U  =      M  -  2  M' 

HI  =      M-       M' 

IV  =      M—3M' 

V  =  '2  M  -       M' 

VI  =      M 

VII  =  2  M  -  3  M' 

VIII  =  3  M  -  2  M' 

IX  =  3  M  -  4  M' 


X  = 

XI  = 
XII  = 

XIII  = 

XIV  = 
XV  = 

XVI  = 
XVII  = 


M  -  4  M' 

3  M  -      M' 

4  M  —  3  M' 
M  —  2  M' 
M  -3M' 
M  -      M' 

3  M  -  5  M' 

4  M'  —  5  M' 


XVIII  = 

XIX  = 

XX  = 

XXI  = 

XXII  = 

XXIII  = 

XXIV  = 
XXV  = 


5  M  -  3M' 

4  M  -     M' 
5M-2M' 

5  M  -  4  M ' 
2  M  -  5  M' 

-  2  M  -     M' 
5M-GM' 

6  M  -  5  M' 


The  perturbations  of  the  rectangular  coordinates  in  units  of  the  Sixth  Decimal  (the  plane  of  the  orbit 
of  Harmonia  being  the  fundamental-plane)  are : — 


0  M 

1  M 

2  J\l 

3  .If 

4  M 

1 

2  I 

3  1 

4  I 

II 

'>  II 
3  II 

III 

2  III 

3  III 
'4  III 

5  III 

IV 
2  IV 


-  3.10* 
+  0.05* 
+  l.Obt 
+  0.07* 


+733.1 
-2G5.2 
-222.8 

-  14.5 

-846.3 

-  2.7 

-  0.9 

+  4J.4 
v+147.4 
+119.8 
+  2.7 
+  0.5 

-377.4 

-  0.9 


+412.52* 
+  22.89J 
+  1.26* 
+  0.06* 

+  146.4 

-  132.3 
-    83.1 

4.0 

-  348.9 

5.1 

-  0.4 


11.5 

75.3 

28.3 

1.7 

0.5 


-    85.0 


-  11.38* 
-412.35* 

-  22.88* 

-  1.26* 

-  O.OGi 

+  147.2 

-  132.1 

-  83.0 

4.0 

-  344.6 

-  15.0 

-  0.4 

+  15.9 

-  69.6 

-  27.8 

-  1.7 

-  0.5 

-  85.1 


1.06* 
0.07* 


-  728.9 
+  265.5 
+  222.8 
+  14.5 

+  847.5 
+  41.1 
+  0.9 

+  31.5 
+  136.1 
+  119.6 

+  3.0 
+  0.8 

+  378.4 

+      0.9 


+18.94* 
+  0.44* 


+  13.5 

-  1.9 

-  0.0 


+  23.0 
+    5.6 


-  2.3 
+    1.1 

-  0.8 


+    4.4 


+  2.7 

-  1.4 

-  0.4 


+  9.3 

+  2.8 


-  1.3 

+  0.9 

-  0.4 


+  2.0 


fi 

1\ 

fi 

CO* 

•in 

cot 

lin 

cos 

sin 

V 

-328.0 

-    67.3 

+    67.5 

-  328.6 

-    5.6 

-     1.1 

a  v 

+  16.0 

+      6.6 

-      0.6 

+     I.V.i 

0  VI 

-    8.1 

+     l.H 

-     1.4 

1    V  1 

+112.0 

+111.5 

+     5.3 

•J  VI 

+    6.1 

-    1  -' 

+     1.1 

+    6.1 

VII 

+  93.4 

+  11.3 

-1237 

+260.6 

-  30.5 

-  19.9 

2  VII 

1.1 

-     1.4 

1.4 

+    1.6 

Mil 

+205.6 

+  Ki  1 

-  85.0 

+205.2 

-     1.0 

-    0.4 

IX 

-  27.4 

-  14.9 

-  15.7 

+    3.8 

-     1.5 

-     1.5 

X 

+  32.4 

-    0.7 

-     0.7 

-  32.3 

XI 

-  21,'.-' 

-    4.7 

+    4.8 

-  22.4 

XII 

+  20.7 

+  10.2 

-  10.1 

+  20.5 

XIII 

-    9.8 

-    3.9 

-    3.8 

+    9.8 

XIV 

-    9£ 

-    3.5 

-     3.5 

+    9.6 

XV 

-    2.5 

+  15.0 

+  16.0 

+    2.5 

' 

XVI 

-    4.8 

-    3.3 

-    3.3 

+    4.1 

XVII 

-    3.1 

-    4.6 

-    5.0    . 

+    3.6 

\VIII 

+    1.6 

+    0.9 

-    0.9 

+     1.6 

MX 

-     1.3 

-    0.3 

+    0.3 

-    1.3 

XX 

+    1.0 

+    0.4 

-     0.4 

+     1.0 

X  XI 

+     1.7 

+    1.9 

-    1.8 

+     1.7 

.XXII 

+    1.2 

-    0.9 

-    0.9 

-    1.3 

XXIII 

-    0.8 

+    0.5 

+     0.5 

+    0.8 

XXIV 

-    0.8 

-    1.5 

-    1.6 

+    1.3 

XXV 

4-         .1    -, 

+    0.7 

-    0-7 

+    0.5 

Elfmaitt. 

1863,  Jan.  0,  Washington  Mean  Tiim-. 

0         /             //                                                                                                                                       „ 

/       // 

J/  =   186  52  40.5                                                f  =       2  40  13.6 

-  =       051    7.0  »                                              ,,  =  1039".3353 
Q  =     93  34  51.8  f  Ml  •*  **•                    |og  a  =      0.355500 

»  =       45  48.4 

The  following  Normals  arc  reduced  to  the  mean  equinox  1863.0. 

Berlin  M.  T. 

"                             •'                        Berlin  M.  T. 

a 

,1 

1856  April 

+  5    41  lie       1861  December  27.5 

78  3o     BJJ 

+i>3    «  3/'.4 

7  Soplemb. 

0  ]-:',       1883  M.u 

'->I7    4  58.0 

-  8  !>l   L"J  - 

1-     •   1  .          -. 

1  !'•    1",    1                     +l!l  M   1II.7         l-.l    II,  ,  .,!.,  . 

17  41  34.7 

-  0  49  44.!) 

Julr 

-24  47 

and  they  arc  rcprcsentc.!  l.y  tin-  Tal.l.  ,  uiili  thu  followinu'  r.  -^iiluals  :-— 

. 

A  o  co§  t                           A  <J                                              A  o  cog  <5 

A  i 

-:: 

n 

+0.3 

:•"                       —0.3                                      —4.7 

+2.9 

+"'»                                                                            +5.0 

+  1.7 

+fi.l                         .  :;s 

Example  for  computing  a  Place  from  the  Tables. 
1866,  March  ld.5,  Berlin  M.  T.=March  ld  5"  58m  15»  Washington  M.  T. 


log  7—1 — 


log  e 

8.668304  9.959502  0.354557 

We  will  refer  the  place  to  the  mean  equinox  1863.0.     From  Table  V  we  take  the  logarithms, 


cos  (z,  z) 

9.998741 

and  from  Table  VI  the  constants, 


cos  (T/!  z)        cos  (zt  z) 

8.220160n  8.870363 


cos  ^  y) 
8.646290 


cos  (1/1  y) 

9.963134 


O  /  II 

90  57  13.9 


C' 

o     /        // 

351  7  37.2 


cos  (z,  y) 

9.594004w 


log  sin  a 
9.998801 


COS   (Z!  Z) 

8.788935rc 


COS  (j/i  Z) 

9.596393 


COS   (Zi  Z) 

9.962224 


log  sin  A 

9.963641 


1866 

March 

1  day 

5  hours 

58  minutes 

15  seconds 


1866 
March 
1  day 
6  hours 


1»66 
March 
1  day 
6  hours 


1866 
March 
1  day 
6  hours 


2  46  26.5 

=  mean  anomaly,  and  t  =  time  since  1863.0  are  taken  from  Table  I. 

M  t 


143  17  51.95  +3.00068 
17  2  0.78 
17  19.33 
3  36.53 

41.86 

^ 0.18 

160  41  30.63     +3.16553 


0.16154 
0.00274 
0.00057 


1- 


cot 


•cot 
M  =  cot 


M 


80  20  45.3 


_  v'      81  11  28.8 

v'    162  22  57.6 

From  Table  II.  c-  1     4.4 

v      162  21  53.2 

COS  V 

e  cos  v 
1 +  e  cos  v 
r 
Formation  of  the  Arguments  from  Table  III.* 


log  sin  c 
9.601621 


9.230726 
9.190228 


—0.044402 
0.955598 


I. 

86.12 
355.10 
359.92 
359.98 

81.12 
X. 

127.8 

357.4 

0.0 

0.0 

125.2 

XIX. 

399 

63 
1 

0 


II. 

I!  15.54 
7.23 
0.12 
0.03 

322.92 

XI. 

156.0 

46.2 

0.8 

0.2 

203.2 
XX. 

169 

75 

1 

0 

245 


HI. 

229.42 
12.31 

0.21 
0.05 

241.99 
XII. 
111.5 
53.2 

0.9 
0.2 

165.8 
XXI. 

341 

65 

1 

0 

47 


IV. 

41.65 

2.32 

0.04 
0.01 

44.02 

XIII. 

28.9 
333.2 
359.5 
359.9 

1.5 

XXII. 

357 
9 

0 
0 

6 


V. 
12.71 

29.16 
0.49 
0.12 

42.48 

XIV. 

115 

328 

359 

0 

82 
XXIII. 

160 

321 

359 

0 

120 


VI. 

143.30 
17.03 

0.29 
0.07 

160.69 
XV. 
303 

338 
0 

0 

281 
XXIV. 

153 

56 

I 

0 

210 


VII. 

1.S4.9 

19.4 

0.3 

0.1 

204.7 

XVI. 

140 

26 

0 

0 

166 
XXV. 

210 

78 
1 
0 

289  ' 


VIII. 

242.1 

41.3 

0.7 

0.2 

234.3 

XVII. 

284 

44 
1 
0 

329 


9.979096  n 
8.647400  n 
9.980276 
0.37428  f 

IX. 

54.4 
31.5 

0.5 

0.1 

86.5 
XVIII. 

255 

70 

1 

0 

326 


"The  arguments  being  expressed  in  degrees  and  decimals,  363,  720,  or  1080  must  he  suhtracted  when  one  of  the  sums 
greater  than  one  of  those  numbers. 


f 

'/' 

e 

Terms  with  I 
I 
11 
111 
IV 
V 
\l 
VII 
VIII 

IX 

\ 
\i 

All 
Mil 
A  IV 
XV 

\M 
\\  II 
AVIII 
XIX 
\\ 
XXI 
\\ll 
\\lll 
\  \l\ 
\X\ 

f,  V,  f 

+ 
IBM 

634.6 

9U 

22.2 
U 

o.a 
ii 

A3 

1.3 

330.6 
279.4 

1  >'-•_• 
:i|.:t 

16.8 
19.1 

IT.:, 
9.9 
4.8 
IU 

05 

1.3 
0.8 

0.5 

••• 

ua&a 

DBJ 

20a.6 

:r,.T 
3.8 

2.6 

4.3 
14.7 

S3 
0.3 
4.1 

0.2 

05 
0.8 

664.2 

830  1 

HMU 

BJ9.7 

26.1 

:!.-> 

• 

6.0 
1.6 

0.7 
1.0 

0.6 

+ 

19.0 
6.8 

1  1  .r. 
1.6 
4.5 

35.9 
0.1 

4.9 
6.3 

1.6 

sin  (.«'  +  r)       253  19    7.1       9.U8i:!-'7« 
r  gin  n                                0.373082 
z                                0.3544il'.<» 

sin  (B>  +  r)       165    8  19.7      9.409050 

r  sin  b                                (l.:«7!>-.'-.' 
y                                9.746:  '7-.> 

sin  (C'+r)       153  29  30.4      9.6411652 

r  sin  c                                 !'.'.I7.-)902 
z                              9.625554 

y          +0.5.V-l::t 
V           -         399 
K               :;:«;:! 
A  cos  <)'  sin  a1          +0.264672      !>.  I-J-J7«H 

z          -2.261563 
f          -         236 

X          +0.1)38542 
A  cos  d'  COB  a'          -1.323257      0.12l644n 

cos  a'                                   ii.'.i'.M  !-,'« 
tan  a>       Kirf  41  21.1       0.301064n 

:           +0.422-J:tr. 
f                        7!» 
Z           -0.127-J'.':* 
Asinii'           +0.294863      !M> 
A  cos  d'                                 0.1301(i-J 
cos  &'                                  9.1te!i-7-,! 
tan  /,'       +12  19  32.2      03394 

A                                 0.140-.':  nt 

Reduction  to  the  npp.  ci|iiiin>x. 

;/ 
/          +       12.24 

e                         i.oo.v,' 
<;                  16 

sin  (G'  +  a')               22(5  r.7          !'  -lili-,, 
tan  d'                                     9.3395 

11  ID:< 
-34 

I:;—  -; 
75 

1517J2 
^39 

l'.Ui).7 
3.5 

7:'  1 
+  0 

12.8 
6.6 

co»(xtz)?       -    247.2 
ccw  (y,  z)  J       +        6.5 

co§  (:,  i)  ?       +        4.9 

f       -    235.8 

co,(xl9)f       -      H.O 
eo»(yi»)?'       -    361.5 
co.  (r,  y)  C       -      S6.1 

1.62          0.2085* 
A  o'           +      10.62 

cos(C'  +  o')                     /(              !i.SI4-,'« 
Ad'          -        6.1)1          (>  -:!'.>!» 

a       168  41  3l'.7 
(i       +1-J  111  2r..:t 

17        -    396.6 

co»(i,s)f       +      I:.-.' 
co.(y,i),'              IV,  | 

CO.                                *         1,1    1 

-     :  •  i 

TABLE     I  . 

FOR  THE   MEAN  ANOMALY. 

The  times  are  referred  to  the  meridian  of  Washington. 

Years. 

M 

1 

Years. 

M 

t 

18505 

168  56  49.43 

-  6.99795 

1879 

0          /        // 

74     3  55.95 

+16.00000 

1657 

274  19  36.82 

5.99863 

18805 

179  43  52.67 

17.00205 

1858 

19  42  14.20 

4.99932 

1881 

285     6  30.06 

18.00137 

1859 

125     4  51.59 

4.00000 

1882 

30  29     7.44 

19.00068 

18605 

230  44  48.31 

2.99795 

1883 

135  51  44.83 

20.00000 

1861 

336     7  25.69 

1.99863 

18845 

241   31  41.55 

21.00205 

1862 

81  30     3.08 

-  0.99932 

1885 

346  54   18.93 

22.00137 

1803 

180  52  40.46 

0.00000 

1886 

92  16  56.32 

23.00068 

18645 

292  32  37.18 

+  1.00205    ' 

1887 

197  39  33.70 

24.00000 

1865 

37  55  14.56                       2.00137 

18885 

303  19  30.42 

25.00205 

1866 

143   17  51.95 

3.00068 

1889 

48  42     7.80 

26.00137 

1867 

248  40  29.33 

4.00000 

1890 

154     4  45.19 

27.00068 

18685 

354  20  26.05 

5.00205 

1891 

259  27  22.57 

28.00000 

1809 

99  43     3.44 

6.00137 

18925 

5     7  19.29 

29.00205 

1870 

205     5  40.82 

7.00008 

1893 

110  29  56.68 

30.00137 

1S7J 

3JO  28  18.21 

8.00000 

1894 

215  52  34.00 

31.00068 

18725 

56     8   14.93 

9.00205 

1895 

321   15  11.45 

32.00000 

1873 

161   30  52.31 

10.00137 

18965 

06  55     8.17 

33.00205 

1874 

266  53  29.70 

11.00068 

1897 

172  17  45.55 

34.00137 

1875 

12  16     7.08 

12.00000 

1898 

277  40  22.94 

35.00068 

18765 

117  50     3.80                     13.00205 

1899 

23     3     0.32 

36.00000 

1877 

223  18  41.18 

14.00137 

19005 

128  42  57.04 

+37.00205 

1878 

328  41   18.57 

+15.00068 

Month*. 

M                                    t 

Days. 

M 

t 

,    January    . 

o    o    o.oo              +  o.ooooo 

1 

o       /      // 
0   17   19.34 

+  0.00274 

February 

8  56  59.39                 *    0.08488 

2 

0  34  38.67 

0.00548 

March 

17     2     0.78 

0.16154 

3 

0  51   58.01 

0.00821 

April 

25  59     0.18                       0.24042 

4 

1     9  17.34 

0.01095 

May 

:!4   38   40.24                         0.32850 

5 

1   26  30.08 

0.01369 

June 

43  35  39.63                       0.41344 

6 

1  43  56.01 

0.01643 

July 

52   15   19.C!)                         0.49558 

7 

2     1   15.35 

0.01917 

August 

(ii    12  19.08                       0.58046 

8 

2  18  34.68 

0.02190 

September 

70     9   18.48                       0.66534 

9 

2  35  54.02 

0.02464 

October 

78  48  58.54                       0.74748 

10 

2  53  13.35  . 

0.02738 

November 

87  45  57.93                       0.83236 

20 

5  46  26.70 

0.05476 

December 

96  25  37.!)!!                    +  0.91450 

.     30 

8  39  40.05    • 

+  0.08214 

In  Bissextile  Years  one  day  must  be  subtracted  from  the  date  in  the  first  two  months. 

8 


TABLE     I.—  Concluded. 

FOR  THE   MEAN  ANOMALY. 

The  limes  are  referred  to  the  meridian  of  Washington. 

Hours. 

M 

' 

Hours. 

M 

' 

1 

0  43.31 

+0.0001  1 

13 

i      n 
:>  22.98 

+0.00149 

1 

1   -Jfi.ffl 

o.ooo-j:) 

14 

10     6.28 

0.00  ICO 

3 

2 

O.OOOM 

15 

10   49.59 

0.001  7  'J 

4 

i.v.'-J 

0.00046 

16 

11   32.90 

0.00183 

5 

3  36.53 

0.00057 

17 

12  16.20 

0.00195 

6 

4   19.84 

0.00069 

•         18 

12  59.51 

0.00206 

7 

5     3.14 

0.00080 

19 

13  42.81 

0.00218 

8 

5  46.45 

0.00092 

20 

ii  -ji  ;.r_' 

0.00229 

9 

6  2!>.;:. 

0.00103 

21 

15     9.43 

0.00241 

10 

7   13.06 

0.00114 

n 

15  52.7:! 

0.00252 

11 

7  56.37 

0.00126 

23 

16  36.04 

0.00964 

II 

8  39.67 

+0.00137 

M 

17  i!i.:u 

0.00275 

M 

M 

For  Minutes. 

For  Seconds. 

For  Minutes. 

For  Seconds. 

1 

o'.72 

n 
0.01 

31 

22.37 

n 
0.37 

2 

1.44 

0.02 

32 

23.10 

0.38 

3 

2.16 

0.04 

33 

23.82 

0.40 

4 

2.89 

0.05 

34 

24.54 

0.41 

1 

3.61 

0.06 

35 

KJH 

0.42 

i 

4.33 

0.07 

36 

0.43 

7 

5.05 

0.08 

37 

26.70 

0.45 

8 

5.77 

0.10 

38 

•             27.43 

0.46 

9 

6.50 

0.11 

39 

28.15 

0.47 

10 

TJU 

0.12 

40 

28.87 

0.48 

11 

7.94 

0.13 

41 

99.60 

0.41) 

13 

•  '  '; 

0.14 

40 

30.31 

0.51 

13 

9.38 

0.16 

43 

31.03 

0.52 

14 

10.10 

0.17 

44 

31.76 

0.53 

15 

10.83 

0.18 

M 

39.48 

0.54 

16 

11..  V. 

0.19 

46 

33.10 

0.56 

117 

12.27 

0.20 

47 

33.91 

0.57 

18 

0.22 

1- 

34.64 

0.58 

19 

111.71 

0.23 

40 

36.37 

0.60 

90 

14.43 

0.24 

50 

36X19 

0.60 

16.10 

0.25 

61 

:u;>i 

0.61 

M 

K.  -- 

".•.•' 

M 

37.83 

0.62 

S3 

0.28 

53 

O.C4 

N 

0.29 

r.4 

:',-.:  17 

0.65 

;-. 

0.30 

K 

30.70 

0.66 

••'• 

0.31 

40.41 

0.67 

'-: 

0.32 

69 

41.11 

• 

0.34 

41Jt 

0.70 

,. 

0.35 

1  1 

0.71 

M 

GO 

43.31 

0.72 

TABLE    II. 

FOR  THE 

CORRECTION  c  TO  BE  ADDED  TO  THE  AUXILIARY  ANOMALY  »'. 

Argument  =  Jlf.     For  M  >  180°  the  Argument  is  360°  —  M,  and  the  sign  of  c  is  to  be  reversed. 

Arg. 

c 

Diff. 

Arg. 

c 

Diff. 

Arg. 

c 

Diff. 

Arg. 

c 

Diff. 

o 

11 

H 

0 

'II 

ii 

O 

„ 

ii 

O 

ii 

ll 

o 

0.00 

45 

+1  13.90 

90 

-  13.77 

135 

-109.08 

1 

+     4.30 

+4.30 

46 

113.40 

-0.50 

91 

17.62 

-3.85 

136 

108.67 

+0.41 

2 

8.59 

4.29 

47 

112.75 

92 

21.43 

3.81 

137 

108.14 

0.53 

3 

12.86 

4.27 

48 

111.95 

0.80 

93 

25.20 

3.77 

138 

107.49 

0.65 

17.11 

4.25 

49 

111.01 

0.94 

94 

28.93 

3.73 

139 

106.72 

0.77 

5 

21.35 

4.24 

50 

109.92 

1.09 

95 

32.63 

3.70 

140 

105.84 

.    0.88 

6 

25.56 

4.21 

51 

108.68 

1.24 

96 

36.29 

3.66 

141 

•  104.84 

1.00 

4.17 

1.38 

3.60 

1.11 

7 

29.73 

52 

107.30 

97 

39.89 

142 

103.73 

8 

33.85 

4.12 

53 

105.79 

1.51* 

98 

43.44 

3.55 

143 

102.50 

1.23 

9 

37.92 

4.07 

54 

104.15 

1.61 

99 

46.92 

3.48 

144 

101.17 

1.33 

10 

41.93 

4.01 

55 

102.37 

1.78 

100 

50.34 

3.42 

145 

99.73 

1.44 

1] 

45.90 

3.97 

56 

100.45 

1.92 

101 

53.70 

3.36 

146 

98.17 

1.56 

12 

49.80 

3.90 

57 

98.41 

2.04 

102 

56.99 

3.29 

147 

96.51 

1.66 

13 

53.62 

3.82 

58 

9G.24 

2.17 

103 

60.20 

3.21 

148 

94.75 

1.76 

3.75 

2.28 

3.14 

14 

57.37 

59 

93.96 

104 

63.34 

149 

92.89 

' 

15 

61.03 

3.66 

60 

91.56 

2.40 

105 

66.40 

3.06 

150 

90.93 

1.96 

16 

64.61 

3.58 

Cl 

89.05 

2.51 

106 

69.37 

2.97 

151 

88.87 

2,06 

17 

68.10 

3.49 

62 

86.42 

2.63 

107 

72.26 

2.89 

152 

86.72 

2.15 

18 

71.49 

3.39 

63 

83.69 

2.73 

108 

75.05 

2.79 

153 

84.48 

2.24 

19 

74.77 

3.28 

64 

80.86 

2.83 

109 

77.75 

2.70 

154 

82.14 

2.34 

20 

77.96 

3.19 

65 

77.93 

2.93 

110 

80.3G 

2.61 

155 

79.72 

2.42 

21 

81.04 

3.08 

66 

74.90 

3.03 

111 

82.86 

2.50 

15G 

77.22 

2.50 

22 

84.00 

2.96 

67 

71.78 

3.12 

112 

85.26 

2.40 

157 

74.64 

2.58 

23 

86.84 

2.84 

68 

68.58 

3.20 

113 

87.57 

2.31 

158 

71  .97 

2.67 

24 

89.55 

2.71 

69 

65.30 

3.28 

114 

89.77 

S.20 

159 

69.23 

2.74 

25 

92.14 

2.59 

70 

61.94 

3.36 

115 

91.86 

2.09 

160 

66.42 

2.81 

26 

94.  GO 

2.46 

71 

58.51 

3.43 

116 

93.84 

1.98 

101 

63.54 

2.88 

27 

90.93 

2.33 

72 

55.02 

3.49 

117 

95.71 

1.87 

162 

60.59 

2.95 

28 

99.12 

2.19 

73 

51.47 

3.55 

118 

97.47 

1.76 

163 

57.58 

3.01 

29 

101.18 

2.06 

74 

47.85 

3.62 

119 

99.11 

1.64 

1G4 

54.51 

3.07 

30 

103.10 

1.92 

75 

44.18 

3.67 

120 

10Q.G4 

1.53 

165 

51.38 

3.13 

31 

104.87 

1.77 

70 

40.47 

3.71 

121 

102.08 

1.44 

166 

48.20 

3,18 

32 

106.50 

1.63 

77 

36.71 

3.76 

199 

103.34 

1.26 

167 

44.97 

3.23 

33 

107.98 

1.48 

78 

•)  70 

32.92 

123 

104.51 

1.17 

168 

41.69 

3,28 

34 

109.31 

1.33 

7!) 

29.09 

124            105.57 

1.06 

169 

38.37 

3.32 

35 

110.50 

1.19 

80 

25.23 

3.86 

125           106.50 

0.93 

170 

35.01 

3.36 

36 

111.53 

1.03 

81 

21.36             3'8? 

126 

107.31 

0.81 

171 

31.61 

3.40 

37 

112.41 

0.88 

89 

17.47 

127           108.00 

0.69 

172 

28.18 

3.43 

38 

113.13 

0.72 

83 

13.56 

128           108.56 

0.56 

173 

24.72 

3.46 

39 

113.70 

0.57 

84 

9.64 

129           109.00 

0.44 

174 

21  .24 

3.48 

40 

114.12 

0.42 

85 

5.72 

130 

109.32 

0.33 

75 

17  74 

3.50 

41 

114.38 

0.36 

86 

+     1.80             3'92 

131 

109.52 

0.20 

76    |          14.21 

42 

114.49 

+0.11 

87 

-    2.11             3'91 

132           109.59 

-0.07 

77             10.  G7 

3.54 

43 

114.45 

-0.04 

88 

6.01             3'9° 

133            109.54 

+0.05 

78               7.12 

3.55 

44 

114.25 

0.20 

89 

9.90             3'89 

134            109.37 

79         -    3.56 

45 

+113.90 

—0.35 

90 

-  13.77 

135   1      -109.08 

+0.29 

180               0.00 

+3.56 

COt  4  0' 

1  —  e 
=  .    .      cot  J  M 

True  Anomaly  r  =  r'  +  c                           log  .  -T-|  =  9.959502 

r 

p 

log;,  =  0.354557                             log  ,  =  8.668304 

~   1  -f-  F  COS  V 

II- 


10 


TABLE    11 

I. 

FOR  TIIK  AHCl  MENTS. 

A.     For  the  different  Yean.     The  times  are  referred  to  the 

meridian  of  Washington. 

Yean. 

t 

II. 

III 

IV. 

V              VI. 

VII. 

Mil 

l.\ 

X. 

XI. 

XII. 

XIII. 

4 

o 

o 

o 

o 

0 

o 

O 

o 

0 

0 

o 

0 

i-:-;/; 

29.54 

88849 

198.49 

7.43     168.95 

66.5 

9064 

265.0 

287.1 

176.4 

44.4        2.-.H.1 

i  -:,: 

874.78 

273.51 

'.171.97 

1-7.  -7     -.'7l.:n 

186.3 

101.4 

99.8 

271.2 

102.2 

14.9          84.1 

1868 

317.1- 

286.37 

8.30      19.70      306.1 

356.9 

294.7 

9564 

28.0 

31.-,.:,        278.1 

i  -:,  • 

2.20 

6164 

300.77 

188.72      1-J5.0.S         65.9 

859.4 

1994 

939.3 

313.8 

3lli.O        II'J.O 

i-..'/; 

898.18 

47.0.-, 

138.90 

:u.vji 

9.65    -j:«i.7.-.      186.0 

148.5 

3944 

993.  1 

240.4 

•J-7.1       305.6 

1861 

•  91.T8 

•Ji3.!>r, 

329.61 

190.08     33li.l-J       IW5.7 

44.0 

169.7 

207.4 

166.2 

958,0 

139.5 

I  -.;•_• 

207.50 

136.51 

289.00 

34441 

10.50       M.50 

299.5 

3544 

191.5 

92.0 

998.5 

333.5 

I77.]- 

1-1.-J3 

4.06 

:;.-.-.  II 

190.93     186.88 

185.3 

1964 

189.3 

175.6 

17.8 

199.0 

1674 

!   i-  1/)' 

I4C..77 

7H.31 

12.85 

ll.-.i      .':'•.'.  :.l 

305.4 

91.2 

24.7 

159.6 

304.4 

170.5 

1.0 

i-..-, 

in;,  ii 

•J7H.-1 

I5I.3T, 

27.25 

r  .<•;.•£>     37.92 

054 

346.6 

9194 

143.7 

230.2 

141.0 

195.0 

1866 

96.19 

:u  :,.:,  i 

1146 

12.71     143.30 

184.9 

949.1 

54.4 

1974 

156.0 

111.5 

38.9 

I-..7 

040 

304.47 

56.05 

193.14     248.67 

304.7 

137.G 

9494 

111.8 

81.8 

89.  1 

999.9 

!-..-/,' 

45,11 

19.79 

70.49 

14.06     35I.:H 

64.8 

33.8 

84.6 

964 

8.4 

534 

56.4 

!  i860 

94.78 

94.06 

r.'i..-,n     99.79 

1844 

9994 

279.4 

80.0 

294.2 

94.0 

250.4 

1870 

3-JI.73 

i  :u.5i; 

169.83 

99.29 

1  l.'.i-J     -J.I.-..KI 

304.4 

184.7 

114.2 

64.0 

220.0 

354.6 

-I.I 

1-71 

•."i.ii 

179.29 

21  1.-- 

113.7(1 

195.35    310.47        64.2 

80.2 

309.0 

48.1 

145.8 

395.1 

978.4 

i-;-.'/; 

•J-J  1.11 

180.14 

128.14 

16.27       50.14       1-1.:'. 

336.4 

144.4 

39.1 

7-.'.  1 

-.".Hi.5        111.9 

1873 

36.19 

n.'.:.i 

196.71     1C.I..VJ      :iii4.l 

9314 

3394 

16.2 

358.2 

267.1        305.8 

1-71 

3I3..-.H 

iiii.-ji 

[KM 

17.13     -JIH5.89 

63.8 

127.4 

174.1 

0.3 

284.0 

237.  (i         139.S 

1875 

173.03 

i<>.->.> 

171.31 

19756       12.27 

183.6 

994 

34 

344.4 

209.8 

i        333.8 

ienB 

14949 

4:1.17 

•ji;o..v, 

186.78 

18.4^     117.-.I3 

303.7 

8794 

9044 

398.4 

136.4 

179.C         IC.7.3 

1877 

II  -J.-JI 

200.19 

198.91     223.31 

63.5 

174.5 

39.1 

319.6 

62.2 

150.1              1.3 

1878 

81.97 

n-j.ti-j 

81169 

l'.i.3l     .i-.'-..;;i 

183.3 

70.0 

9334 

996.5 

348.0 

120.7 

195.3 

1879 

SIM 

I77.:r, 

l-J.-i.7l 

l:t'.'.77        7I.H7 

303.1 

3964 

68.7 

280.6 

273.8 

914 

99.9 

i--  >/; 

81.93 

WOJM 

84843 

20.70      I7H.73         C.3.-J 

991.7 

964.1 

964.7 

200.4 

69.6 

999.7 

i--i 

86743 

•JOI.I-J     '.'-.-,.11        l-.'.'.i 

117.1 

99.0 

•JI-.7 

126.2 

33.9 

.Mi.  7 

I--.- 

n  '..•.- 

IIII.IM 

35  1.07 

97943 

•,'I..V,       30.111       302.7 

I-M; 

293.8 

939.8 

59.0 

3.7         -J.-.0.7 

l--: 

:{.--:.:(- 

286.64 

-J.il.ii-     i:i:..-r.       <;•>.:, 

268.1 

1984 

216.9 

337.8 

331.2           -1.7 

i--i/; 

4143 

141.38 

3014? 

•J-J.!MI      -J1I..VI         l-.'.il 

1644 

324.0 

200.9 

964.4 

305.7 

9784 

i---. 

91643 

31848 

•J03.33     3IC.1H       302.4 

59.8 

i:.-.- 

185.0 

1904 

276.2 

112.1 

:--.. 

991.48 

•-':!.  7.  ;      I.-.'.-.'-        .;•.'.! 

315.2 

3634 

169.1 

116.0 

946.7 

306.1 

1--7 

16847 

17:..  IM 

314.2- 

•joi.  in    nc.iii;      1814 

•JI0.7 

i.  --•..-. 

153.1 

41.8 

•JI7.3 

140.1 

w»B 

I3-.I7 

-.'.-..II      303.33       3ii-J.(l 

1064 

137.9 

398.4 

1—  .7         333.6 

!--.. 

III-.  II 

I.  v;.-i 

18.19 

•-•o.-,..-,|         I-.70          614 

•J.i 

218.7 

191.3 

9544 

I.Vi.-J        167.6 

I-,, 

77.  -1 

3011.71 

•j:i  -  ' 

8748 

:     I.-.4.08 

181.6 

53.6 

106.3 

1804 

l-J'.t..-            1.6 

I".H 

. 

ILU 

301.4 

1684 

9484 

89.4 

105.8 

100.3         1115.5 

i  -  •  .•  /; 

17.ll- 

6846 

:..rj 

614 

in.:, 

83.7 

7:1.1 

32.4 

71.7 

89.0 

MM 

346.78 

-l.lll 

70.71; 

-'07.7.-,     110.50 

181.3 

305.0 

9784 

:,7.r, 

318.2 

49.3 

993.0 

i-<i 

3ir,..|:: 

198.74 

17941 

-:..  1  7 

-'-.I-     -J  15.88 

801.0 

9004 

113.3 

114 

944.1 

12.8 

.-,7.0 

i-  • 

17.  MI, 

-.'I7.:ir. 

208.61     3-JI.  -.•:. 

064 

•-'.-,.7 

1094 

313.3 

251.0 

i  -  -  /; 

•JI-.3I 

111.01 

180.9 

369.1 

1434 

9.7 

96.4 

311.7 

-1.:. 

1891 

I'.'-  II 

I7.'.3o      300.1 

8474 

33.--.  1 

3534 

894 

885.3 

978,6 

!-,. 

. 

807.76 

M2.7-J 

14941 

:  i;7       no.:, 

1  !:;.! 

1734 

837.9 

30S.1 

956.8 

119.4 

;-  .. 

1-7.77 

157.21 

•Jio.-.'      -.M.II:,      1804 

384 

-.n 

3914 

9384 

306.4 

I7l.li.-i 

3i.7i     i  •.'-.:•.• 

904.8 

203.4 

30(1.0 

1604 

197.8 

139.9 

11 


TABLE  III.—  Continued. 

FOR  THE  ARGUMENTS. 

A.  For  the  different  Years.  The  times  are  referred  to  the  meridian  of  Washington. 

Years. 

XIV. 

XV. 

XVI. 

XVII. 

XVIII.   XIX. 

XX. 

XXI. 

XXII. 

XXIII. 

XXIV.  XXV.. 

16565 

280    221 

o 

294 

0 

103 

0            0 

213     345 

O 

184 

243 

126 

0 

52 

0            0 

302     81 

1857 

83     85 

99 

13 

289 

17 

290 

288 

185 

171 

287    202 

1858 

247 

309 

264 

283 

5 

48 

36 

334 

244 

289 

272     323 

1859 

51 

173 

68 

193 

81 

79 

143 

20 

303 

48 

257     83 

16G05 

214 

37 

233 

104 

158 

111 

250 

66 

2 

167 

243     205 

1861 

17 

262 

37 

14 

234 

142 

356 

112 

61 

286 

228    326 

18G2 

181 

126 

202 

284 

310 

.  f!4 

103 

158 

121 

45 

213 

87 

1803 

345 

350 

7 

193 

26 

205 

209 

203 

179 

163 

197 

207 

16645 

148     214 

171     104 

103' 

237 

316 

250 

239 

282 

183 

329 

1865 

311     79 

336     14 

179 

268 

62 

295 

298 

41 

168 

90 

1866 

115     303 

140 

284 

255 

299 

169 

341 

357 

160 

153 

210 

1867 

279 

167 

305 

194 

331 

330 

275 

27 

56 

278 

138 

331 

18685 

82 

31 

110 

104 

48 

3 

22 

73 

116 

37 

124 

93 

1869 

245    255 

274 

14 

124 

34 

129 

119 

175 

156 

109 

214 

1870 

49     120 

79 

284 

'  200 

65 

235 

164 

234 

275 

94 

334 

1871 

213     344 

243 

194 

276 

96 

341 

210 

293 

34 

79 

95 

18725 

16     208 

48    105 

353     129 

89 

257 

352 

152     65 

217 

1873 

180 

72 

213     14 

69     160 

195 

302 

51 

271 

50 

337 

1874 

343 

296 

17     284 

145     191 

301 

348 

.110 

30 

35 

98 

1875 

147 

161 

182     194     220     222 

47 

33 

170 

148  . 

19 

319 

18765 

310 

25     347     105     297     254 

155 

80 

229 

267 

5 

341 

1877 

113 

249 

151     15     13     286 

261 

126 

288 

26 

350 

101 

1878 

277 

113 

316 

265     89     317 

7 

171 

347 

145 

335 

222 

1879 

81 

338 

120 

194    165    348 

114 

217 

46 

264 

320  j  343 

18805 

244 

202 

285     105     242     20 

221 

264 

106 

22 

306 

105 

1881 

48 

66     90 

15     318 

51 

327 

309 

165 

141 

291 

225 

1862 

211 

290     254 

285' 

34 

82 

74 

355 

224 

260 

276 

346 

1883 

15 

154     59 

195 

110 

114 

180 

40 

263 

19 

261 

106 

18845 

178 

18     224 

105     187 

146 

287 

87 

342 

137 

247 

228 

1865 

342 

243 

28 

15 

263 

177 

34 

133 

41 

256 

232 

349 

1886 

145 

107 

193 

285 

339 

208 

140 

178 

100 

15 

217 

110 

1887 

309 

331 

357 

195 

55 

239 

246 

224 

160 

134 

202 

230 

18685 

112 

195     162 

106    132 

272 

354 

270 

219 

252 

187 

352 

1889 

276 

59     327 

15 

208 

303 

100 

316 

278 

11 

172 

113 

1890 

79 

284 

131 

265 

284 

334 

206 

2 

337 

130 

157 

234 

1891 

243 

148 

296 

195 

0      5 

312 

47 

3G 

249  i  142 

354 

18925 

46 

12 

101 

106     77 

38 

GO 

94 

96 

7 

128 

116 

1893 

210 

236 

265 

16     153 

69 

166 

140 

155 

126 

113 

237 

1894 

13     101     70 

286    229 

100 

272 

185 

214 

245 

98 

357 

1695 

177 

325     234 

196     305 

131 

18 

231 

273 

4 

83 

116 

18965 

340 

189     39 

106     22     163 

126 

277 

332 

122 

69 

240 

1897 

144 

53 

204 

16     98     195 

232 

323 

31 

241 

54 

1 

1898 

308 

277 

8 

266    173    226 

338 

9 

91 

0 

39 

121 

1899 

111 

142 

173 

196 

249     257 

85 

54 

150 

119 

24 

242 

19005 

274 

6 

336 

106     326     289 

192 

101 

209 

237      9      4 

12 


TABLE 

III  .  —  Co  n  tinned. 

FOR  THE  ARGUMENTS. 

It.     Variation*  of  thr  Argument*  for  the  different  Months.     The  times  are  referred 

to  the  meridian  of  Washington. 

M    nth..                     1.                  II. 

III. 

IV.                 V                   VI 

VII 

VIM. 

IX. 

000 

0 

0 

0 

January                          I»HI             0.00 

0.00 

0.00                0.00             0.00 

0.0 

0.0 

0.0 

February                   X>7  4'.' 

<;:t7 

i  •-••-•           I."i.:i2           -  '  • 

III.-.' 

21.7 

I&6 

M:,                         :i5.vi0           :  B 

i-'  1:1 

•-'.:(•-'           2i».i(>         I7.n:i 

1!",4 

41.3 

:u.r. 

April                     :f..             n."-' 

:t:,l            ii.  IK 

99.fi 

634) 

48.0 

M,*                      350.03         H7n 

•:ii,r 

47:1          .v.i.:ti         :u.(i4 

:i'.t,i 

-in 

64.0 

Jim.-                            :t47.46            18.50 

31  JK 

:,;ir,          rii.i         4:i..v.» 

r':. 

105.7 

80.6 

Juiv                      :i44ixi         -.-j-.-r 

:t7'Ji 

7.1:1          99.47        '^.-.H; 

.Vl.l 

126.7 

96.6 

August                     :i!-.>39 

rv:i-|            104.7!»           CI.21 

,..-, 

1  1-  1 

11:1.1 

September                                        1  '77 

4!>.!Hi 

l-.M.ii           70.16 

7!».7 

170.1 

r.-.i.7 

.b«r                :«7.32        33.44 

:>6.i3 

l(l.7:>            134.!>4            7  -.».' 

89.6  . 

191.1 

1  ir,  7 

N        MitM-r                  :«4  .75 

I1.K7            l.-.ll-^i            -7.77 

99.7 

212.8 

IflU 

,,l»r                    33225 

IMIti            11,:,  on           'XZtt 

109.6 

17-  -J 

• 

Month*.                    \                  M 

Ml 

Mil              \  1  \                XV. 

XVI 

XVII. 

XVIII. 

0                                0 

January                           ""            .     "" 

0 

0.0 

I                     , 
o                      o                     o 

0.0                 0                   0 

0 

0 

0 

n 

o 
0 

Februarv                                             -i:1- 

iW.l 

:t|.'..;i             343               348 

14 

n 

37 

March                         :u-,T  1 

:.:t.4 

:K»3.2                          :$38 

M 

41 

70 

April                          :i'.t.  1 

-I  :. 

:iiit.o          :ui            :i-.>7 

-in 

ee 

109 

M 

10f.6 

us 

M 

89 

149 

II-.' 

I3U.7 

•*.<\:.\          -'7:i            :?04 

(W 

119 

180 

Jul»                           3521            141.7 

277.11              -'Ii4                293 

fl 

1:14 

216 

Augu.t                                           I'-." 

I:M  n 

•Ji,:i,-.           -JI-,             -J-l 

!ir. 

i:,7 

253 

mber                                        ll«'-' 

220.0 

-.M;I  1                               270 

inn 

180 

290 

.her                                          21:1.7 

-M7-J 

213                -J.V.I 

vu 

KM 

:WG 

238.0 

221.7              1%                '-'47 

136 

'->-r> 

:i 

>t..T                                                             -''.I   ."• 

m  i 

180              896 

1541 

'-'17 

39 

XXI 

XXII.          XXIII.         XXIV. 

XXV 

Month.                 M  \              \  \ 

0 

January                            0                   (1 

o 
0 

000 

0                     I)                    0 

o 

II 

nary                       33 

34 

:,             :i:t:t              -jit 

41 

Marrl, 

G:> 

;t             :!•-'!               :^i 

n 

April                                                II'. 

1  1 

ii- 

Mar                             1-'-               l.'.l 

in 

III                  '-'-I                  113 

i  - 

m 

M 

.'i             200             1  1:1 

190 

July                                  1  'I 

171 

Auc 

:n 

•-'7  11 

:'.ll 

i  19 

:tv!n 

4-1               160 

H9 

•»l»  r 

337 

4'.'                  I.V.I                 '.>-7 

40 

II 

nit             :u:, 

-n 

In  lliMcxtile  Yean  tubtract  one  day  from  the  dale  in  the  fin!  two  months. 

13 


TA 

BLE 

I  II.  —  Concluded. 

FOR  THE  ARGUMENTS. 

C.     Variations  of  the  Arguments  for  the  different  Days.     The  times  are  referred  to  the  meridian  of  Washington. 

Days. 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

X. 

XI. 

XII.         XIII. 

1 

o 

o 

0 

0 

0 

0 

0 

0 

0 

0 

0 

o                     o 

1 

359.92 

0.12 

0.21 

0.04 

0.49 

0.29 

0.3 

0.7 

0.5 

0.0 

0.8 

0.9          359.5 

2 

359.83 

0.24 

0.41 

0.08 

0.99 

0.58 

0.7 

1.4 

1.1 

359.9 

1.6 

1.8          359.1 

3 

359.75 

0.37 

0.62 

0.12 

1.48 

0.87 

1.0 

2.1 

1.6      !     359.9 

2.3 

2.7 

358.6 

4 

359.67 

0.49 

0.82 

0.16 

1.98 

1.15 

1.3 

2.8 

2.1          359.8 

3.1 

3.6 

358.2 

5       359.53 

0.61 

1.03 

0.20 

2.47 

1.44         1.6 

3.5          2.7          359.8 

3.9 

4.5 

357.7 

6      35!).50 

0.73 

1.23 

0.24 

2.97 

1.73         2.0 

4.2          3.2          359.7 

4.7 

5.4 

357.3 

7       359.42 

0.86 

1.44 

0.28 

3.46 

2.02         2.3 

4.9          3.7           359.7- 

5.5 

6.3 

356.8 

8 

359.33 

0.98 

1.64 

0.32 

3.95 

2.31     :     2.6        5.6          4.3          359.6 

.6.3 

7.2 

356.4 

9 

359.25 

1.10 

1.85 

0.35 

4.45 

2.60         3.0 

6.3 

4.8 

359.6' 

7.0 

8.1 

355.9 

10 

359.17 

1.22 

2.06 

0.39 

4.94 

2.89          3.3 

7.0 

5.3 

359.6 

7.8 

9.0 

355.4 

20 

358.34 

2.45 

4.11 

0.79 

9.89 

5.77         6.6 

14.0 

10.7 

359.1 

15.7 

18.1 

350.9 

30 

35751 

3.67 

6.17 

1.18 

14.83 

8.66     1     9.8 

21.0 

16.0 

358.7 

23.5 

27.2 

346.3 

XV. 

Days.1     XIV. 

XVI. 

XVII. 

XVIII. 

XIX. 

XX. 

XXI. 

XXII. 

XXIII. 

XXIV. 

XXV. 

1 

o 

359 

0 

0 

o 
0 

0 

1 

o 

1 

o 

1 

O 
1 

o 

1 

o 
0 

0 

359 

o 

1 

0 

1 

o 

2 

359 

359 

1 

1 

2 

2 

3 

2 

0 

359 

2 

3 

1! 

358 

359 

1 

2 

4 

3             4 

3 

0 

358 

3 

4 

4        358 

359 

2 

3 

5 

4              5 

4             1 

357 

4 

5 

.->         357 

358 

2 

4 

6 

5             6 

6             1 

357 

5 

7 

13        357 

358 

3 

4 

7 

6             8 

7             1 

356 

6 

8 

7         356 

357 

3 

5 

8 

7 

9 

8 

1 

355 

7 

9 

8         356 

357 

4 

6 

10 

9 

10 

9 

1 

355 

8 

11 

9        355 

357 

4 

7 

11 

10           12 

10 

1 

354 

8 

12 

10        355 

356 

4 

7 

12 

11           13 

11 

2 

353 

9 

13 

20         340 

353 

9 

15 

24 

21 

26 

22 

3 

347 

19 

26 

30        344 

349 

13 

22 

36 

32 

38 

33 

5 

340 

28 

40 

1).     Variations  of  the  arguments  for  the  different  Hours.     The  times  are  referred  to  the  meridian  of  Washington. 

Hours.         I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

X. 

XI. 

i 

XII. 

XIII. 

1 

0.00 

0.00 

0.01 

0.00 

0.02 

0                        0 

0.01         0.0 

0 

0.0 

0                            0 

0.0               0 

0 

0.0 

o 

0.0 

o 
0.0 

2       359.99 

0.1)1 

0.02 

0.00 

0.04 

0.02          0.0 

0.1 

0.0              0 

0.1 

0.1 

0.0 

3 

359.99 

0.01 

0.03 

0.00 

0.06 

0.04         0.0 

0.1 

0.1              0 

0.1 

0.1           359.9    : 

4 

359.99 

0.02 

0.03 

0.01 

0.08 

0.05         0.1 

O.I 

0.1             0 

0.1 

0.2          359.9 

5 

359.98 

0.02 

0.04 

0.01 

0.10 

0.06         0.1 

0.1 

0.1 

0 

0.2 

0.2          359.9 

6 

359.98 

0.03     : 

0.05 

0.01 

0.12     1 

0.07 

0.1 

0.2 

0.1             0 

0.2 

0.2     :     359.9 

7 

359.98 

0.03 

0.06 

0.01 

0.14 

0.08         0.1         0  2 

0.2             0 

0.2 

0.3     ':     359.9 

8 

359.97 

0.04 

0.07 

0.01 

0-.16 

0.10 

0.1 

0.2 

0.2 

0 

0.3 

0.3      (     359.8 

9 

359.97 

0.04 

0.08 

0.01 

0.18 

0-11 

0.1 

0.3 

0.2 

0 

0.3 

0.3          359.8 

10 

359.96 

0.05 

0.08     : 

0.02     ! 

0.21 

0.12         0.1 

0.3          0.2 

0 

0.3 

0.4 

359.8 

20  1    359.93 

0.10 

0.17 

0.03 

0.41     ; 

0.24         0.3        0.6          0.4             0 

0.7 

0.8          359.6 

14 


TABLE    IV. 

PERTURBATIONS  OF 

THE  CO-ORDINATES  IN  UNITS 

OF  THE  SIXTH  DECIMAL. 

TV-ruin  mnltijilifd   with  1.     Argument  = 

•  M. 

Arg. 

Diff. 

f 

Diff. 

?          Diff. 

Arg. 

t 

Diff. 

< 

Diff. 

{'             Diff. 

e 

o 

0 

—  147  'Kl 

0.00 

•I.', 

•fit  I  '2  'M! 

-300.90 

+13 

1 

48.07 

417.  -1 

4-  0.19 

4-1.04 

M 

817.90 

4-  4.94 

4-  5.97 

+0.68 

1 

M.I'.' 

8.06 

1  17.:,.; 

o.« 

47 

;{._).>  ,,.) 

4.82 

-'--.-7 

6.06 

3 

'-••.'.  1  7 

8.05 

117.  HP 

0.43 

-1   l.lll 

1- 

396,79 

4.70 

9H9.73 

6.14 

14.51 

4 

8.04 

||,;  ;,| 

0.59 

1.03 

18 

4.58 

6.21 

0.64    ' 

8.03 

145.76 

0.75 

50 

336.78 

4.45 

6.39 

1 

8.01 

144.86 

0.90 

-,'.117 

51 

:uo.(H 

4.33 

•Jll!  -7 

6.36 

16.16 

7 

.-.l.'.'l 

7.99 

1.06 

1.03 

68 

344.98 

4.30 

•.'",7.  i:> 

i;.  >•; 

0.59 

8 

7.96 

41'.'  .V.i 

1.91 

63 

4.08 

6.49 

9 

7n.ll 

7.94 

441.99 

1.37 

8.10 

M 

:{.v.'!:!  l 

3.95 

944.40 

6.56 

16.74 

7.91 

Mi 

6.62 

10 

1.03 

.">."> 

•  :i:,c,.i:i 

_.)•(-  -^ 

0.54 

11 

4-  1.68 

66 

369.81 

+  3.6S 

.,.,1  |0 

f  6.68 

I5J 

03171 

7.83 

I.I-' 

67 

3.53 

294.38 

J.H 

1C.28 

13 

101.  .14 

7.79 

4:!4.->.' 

1.98 

1.00 

:,- 

366.79 

3.43 

6.77 

0.50 

14 

rw.if.i 

9.13 

69 

3.S9 

210.78 

6.83 

15 

IUM 

'  • 

i-j  '.-.' 

9.97 

R.19 

•j-.j  .,- 

3.17 

Ml 

16.78 

If, 

7.64 

l'.'7.l'i 

9.42 

0.99 

ill 

376.98 

3.03 

198.98 

0.4S 

17 

7.60 

i-j|.-  : 

9.57 

88 

379.18 

2.91 

190.01 

18 

7.54 

199.19 

9.71 

0.11 

03 

381.96 

•i.77 

183.01 

7.00 

17.-.':! 

l  • 

117.  '.'I 

ir.i.-.v, 

.  - 

0.97 

iil 

384.60 

2.64 

176.98 

7.03 

7.41 

3.00 

2.50 

7.07 

0.40 

90 

-l.M.i,-. 

-Hi;.  -.'I', 

06 

4387.10 

-166.91 

•t( 

4-  ..35 

li:i.i:i 

4-  3.13 

7.08 

06 

4-  2.37 

161.80 

4-   7.11 

17.63 

H 

' 

3.27 

0.95 

09 

391.71 

164.67 

7.13 

0.35 

23 

3.41 

08 

•fi't  -i 

2.10 

147..VJ 

7.15 

7.14 

"  Ml 

Ml 

8M 

• 

1  .'.17 

7.17 

17.98 

27 
98 

Otl.40 

i,VV 

9M 
•.90 

• 
6.73 

3.64 
3.81 
3.94 
4.06 

0.99 

70 

71 
-•2 

7:t 

400.89 

•lii-.MU 

1.84 

1.70 
1..-.7 
1.41 

1  -'.V.  II 

118.71 

111.47 

7.19 

JJU 

7.-JI 

0.29 

18,97 

:• 

'.'l-.l:l 

4.19 

0.90 

7  1 

10343 

1.30 

104.99 

7JB 

0.25 

6.64 

4.39 

1.11 

30 
31 

••.".'1.77 

4-6.il 
(.46 

£    M 

4-  4.44 
4.56 

0.87 

n 

77 

•  ioi.-i 
(06,86 
40C.77 

4-   1.05 
0.91 

-  9C.96 

-.1.711 

4-  7.26 

0.19 

33 
34 

•• 

37 

.- 

.Mill 
•J7I.I.! 

6.96 
6.17 
6.06 

- 
1.74 

140.19 

.  •  - 
4.79 
4.90 
S.OI 
5.11 

s.sa 

5.33 

in.  7'.' 

0.83 

11..  V. 

0.80 

i  •_>.:!:, 

7- 

n 

82 

-l 

108.91 

in-.  71 

109.11 
109.40 
M9.63 
108^84 

0.79 

0.53 
0.39 
0.27 
0.13 
4-  0.01 

76.18 
87.88 

r,:t.:t:> 
40.10 
38.85 
3149 

7.28 

tja 

7.26 

7.95 
7.23 

1-.7I 
0.14 

1-.-.-. 
0.08 

18,93 

5.O 

5.43 

—  0.11 

7.22 

41 

a 

43 

II 
1.1 

•  .'-     -' 

• 

ft.  18 
4-  5.06 

...  :  , 

4  5.59 
S.6I 
5.71 
S.80 
4-  5.*9 

0.76 

13.11 
40.79 

-,, 

-- 
-| 
90 

KNB%4I 
109.19 

in-.-  1 
108.36 

-  0.94 
0.36 
0.48 
0.61 
-  0.73 

-  -j  l.in 
10.09 

4-     4.'.'7 
4-  11.37  i 

4-  7.20 
7.18 
7.16 
7.13 
4-  7.10 

40.03 

I-.'.M; 
-0.09 

+18.94 

15 


TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

Terms  multiplied  with  t.     Argument  =  M. 

Arg. 

P 

Diff. 

* 

Diff. 

? 

Diff. 

Arg. 

f 

Diff. 

T,'              Diff. 

v 

Diff. 

0 

0 

90 

+407.01 

+  11.37 

+18.94 

135 

+206.52 

+278.36 

+12.95 

91 

400.10 

-  0.85 

18.45 

+  7.08 

-0.07 

136 

261.47 

-5.05 

282.00    +4'30 

-0.7S 

92 

405.18 

0.98 

25.50 

7.05 

137 

250.36       5'U 

280.88        4'22 

.10 

7.01 

*>  17 

4  12 

93 

404.08 

32.51 

18.87 

138 

251.19 

291.00        4' 

12.23 

.21 

6.98 

5  23 

4  03 

94 

402.87 

39.49 

0.12 

139 

245.90 

295.03 

0.75 

95 

401.54 

.33 

46.44 

6.95 

140 

240.08       5'» 

298.97 

3.94 

.44 

6.92 

5  34 

3.86 

90 

400.10 

53.36 

18.75 

141 

235.34  i          „ 

302.83 

11.48 

.56 

6.88 

5  40 

3.77 

97 

398.54 

60.24 

0.17. 

142 

229.94 

300.00 

0.77 

98 

396.87 

1.67 

67.08 

6.84 

143 

224.49 

5.45 

310.27 

3.67 

1.78 

6.81 

5.50 

3.59 

99 

395.09 

73.87 

18.58 

144 

218.99 

313.86 

10.71 

1.89 

6.75 

5.55 

3.50 

100 

+393.20 

+  80.62 

0.23 

145 

+213.44 

+317.36 

0.80 

101 

391.19 

-2.01 

87.33 

+  6.71 

140 

207.83 

—  5.61 

320.76 

+  3.40 

2.11 

6.66 

5  65 

3.31 

102 

389.08 

93.99 

18.35 

147 

202.18 

324.07 

9.91 

103 

386.86 

2.22 

100.60 

6.61 

0.28 

148 

196.48 

S.70 

327.29 

3.22 

o.ea 

104 

384.53 

2.33 

107.16 

6.56 

149 

190.74        5''4 

330.42 

3.13 

2.43 

6.50 

5  79 

3.04 

105 

382.10 

1  13.00 

18.07 

150 

184.95  I 

333.46 

9.09 

2.53 

6.45 

5  83 

2.94 

106 

379.57 

120.11 

0.32 

151 

179.12 

330.40 

0.85 

107 

376.93 

2.04 

126.51 

6.40 

152 

173.25 

5.87 

339.25 

3.85 

2.74 

6.34 

5.92 

o  ?* 

106 

374.19 

132.85 

17.75 

153 

107.33 

342.00        —  " 

8.24 

109 

371.35 

2.84 

139.13 

6.28 

164 

161.37 

5.96 

344.05 

2.65 

2.95 

6.23 

0.37 

5.99 

2.56 

0.87 

110 

+368.40 

+145.36 

155 

+155.38 

+347.21 

111 

365.36 

-  3.05 

151.52 

+  6.16 

17.38 

150 

149.36 

-6.02 

349.68 

+  2.47 

7.37 

3.14 

6.10 

6  06 

2.37 

112 

302.21 

157.62 

0.41 

157 

143.30 

352.05 

0.88 

3.S4 

6,04 

O  O7 

113 

358.97 

103.00 

156 

137.21 

354.32       —  ' 

3.32 

5.98 

fi  12 

O  17 

114 

355.05 

169.64 

16.97 

159 

131.09  ! 

356.49  ' 

6.49 

3.42 

5.91 

6.15 

2  07 

115 

352.23 

175.55 

0.45 

100 

124.94 

358.56 

0.90 

3.50 

5.85 

6.18 

1  98 

110 

348.73 

181.40 

161 

118.76 

360.54 

117 

345.13 

3.60 

187.17 

5.77 

10.52 

162 

112.56 

6.20 

362.42        1<88 

5.59 

3.68 

5.71 

fi.93 

1  78 

118 

341.45 

J  92.88 

163 

100.33 

364.20 

3.78 

5.64 

6  26 

1  68 

119 

337.07 

198.52 

0.50 

164 

100.07 

365.88 

0.91 

3.86 

5.56 

6.28 

1.59 

120 

+333.81 

+204.08 

10.02 

105 

+  93.79 

+307.47 

4.68 

—  3.95 

+  5.49 

i  —  fi  an 

+  1.49 

121 

329.86 

209.57 

0.54 

166 

87.49 

366.96 

0.92 

4.03 

5.42 

6.32 

1.39 

122 

325.83 

214.99 

107 

81.17 

370.35 

4.12 

5.35 

6.34 

1.29 

123 

321.71 

220.34 

15.48 

168 

74.83 

371.04 

3.76 

4.19 

5.27 

6.36 

1.19 

124 

317.52 

225.01 

0.57 

169 

68.47 

372.83 

0.93 

4.28 

5.19 

6.37 

1    ii-; 

125 

313.24 

230.80 

170 

02.10 

373.91 

120 

308.89 

4.35 

235.92 

5.12 

14.91 

171 

r-  ~i           6'39 
' 

374.90 

0.99 

2.83 

4.42 

5.04 

0.89 

127 

304.47 

240'.96 

0.62 

172 

49.31 

375.79 

0.94 

4.49 

4.96 

6  41 

0.78 

128 

299.98 

245.95 

173 

42.90 

370.57 

4.57 

4.88 

6  43 

129 

295.41 

250.80 

14.29 

174 

«»!"•      «»     '            !*"• 

30.4  / 

377.26 

1.89 

4.64 

4.80 

6.44 

0.59 

130 

+290.77 

+255.00 

0.65 

175 

+  30.03 

+377.86 

0.94 

131 

280.06 

-  4.71 

200.31 

+  4.71 

176 

23.58 

-  6.45 

34  i  +  °'49 

4.78 

4.64 

G.  l.~> 

0  1Q 

132 

981.28 

204.95 

13.04 

177 

17.13 

378.73            9 

+  0.95 

4.85 

6.46 

0  29 

133 

276.43 

209.50 

-0.69 

178 

10.67 

379.05 

0.95 

134 

271.51 

4.92 

273.97 

4.47 

179 

+     4.21 

6.46 

379.20!     °'18 

—  4.99 

+  4.39 

135 

+266.52 

+278.36 

+12.95 

180 

-    2.25  i  " 

+379.29 

0.00 

16 


TABLE    IV.—  Continued. 

I'KKiTKUATIoNS  OF  Till:  CIM.  lililXATKS   IN   1XITS 

OK  'I'lIK  SIXTH    DKC1MAI.. 

Ternn  inultijilicit   with  t.     Argiinn-iit  = 

.V. 

Arg. 

i  Our 

* 

11,  If. 

Diir. 

Arg. 

Diir. 

"' 

Diir. 

Ditr. 

o 

o 

180 

-    •-• 

-f  ^T'.'.'.':' 

0.00  ' 

979.87 

+2d0.37 

i  •_'.•.  >.-, 

1-1 

"    « 

-0.03 

i  -0.95 

896 

977.99 

-5.05 

976.99 

-0.69 

I.VI7        '•" 

0.13 

•.'.'7 

939.90 

4.98 

971.59 

1.41 

,, 

4.55 

i-t 

91.63 

378.93 

-  O.'.i:, 

998 

986.97 

13.64 

l-l 

0.46 

878.61 

u.:n 

0.94 

•-'•J.i 

939.07 

144 

0.4:1 

897.46 

•j:>7  i;i 

1.7S 

i-<; 

6.45 

877.66 

0.53 

1.-  1 

931 

809.17 

4.71 

959.81 

4.80 

1  l.->  i 

187 

17.11 

877.04 

0.63 

0.94 

•-'  ;•,' 

4.64 

947.99 

4.89 

188 

:i7ii.-ti 

0.73 

.)  j;j 

:tn.:ts 

348.95 

I.T. 

189 

0.83 

'.'.-I 

-'.'.4 

316.87 

4.H 

14.01 

6.41 

0.93 

4.41 

8.13 

190 

-Tit 

0.93 

•'  !"> 

-390.98 

-"•'!•'  77 

I'M 

7:1.11.     -••* 

:!7:i..v> 

-  1.03 

894.61 

-4.33 

•'••;  :.:> 

-  Ml 

6.39 

:IT-.'.I-.' 

.11 

:i  :»; 

987 

4.96 

999.98 

15.48 

6.37 

.33 

4.17 

.*..;i  ; 

194 

" 

.33 

0.93 

936 

•j  19 

333.04 

4.10 

916.89 

,'  ll.ll 

8.49 

0.54 

6.33 

.« 

940 

:t  i  u  .-i 

4.01 

16.09 

mi.-i      *'30 

:!r,ii.:u 

.53 

0.91 

941 

;{(.-  |,7 

:i.  '.<-.' 

990.39 

5.60 

0.50 

iii.i-j     *•" 

.63 

949 

3&9I 

3.84 

196.63 

5.67 

.73 

3.75 

."..7  1 

198 

1  1  *  .:»'.* 

itoi'i..-,! 

943 

359.66 

188.91 

n  ;.:>•.' 

193.64 

861.71 

.63 

•.Ml 

:t.^;.:i-j 

3.66 

183.10 

6.93 

1.99 

0.90 

:I.;,T 

:..-'! 

ii.  i:. 

800 

846 

-360^9 

+  177.-.'! 

881 

6.19 

—  9.03 

6.49 

946 

-3.48 

n;  '17 

1   .' 

3fi6.66 

3.13 

\Wt--  - 

3.38 

hi.-..-.'l 

i;.nj 

ii.  n 

•-•    ; 

i  !-.:r,      '•" 

948 

:!7n  D.I 

Ml 

159.16 

6.09 

884 

.•  : 

i-.i.n.      •'" 

6.07 
6.04 

851.19 

3.31 
9.41 

9.61 

7.87 

0.87 

-.'.'I 

24!) 
950 
951 

376.3S 
379.31 

3.19 
3.09 
3.99 
9.90 

153.00 

1  IH..-.1 

134.17 

(i.i:. 
5.91 

i,  •_•- 
6.34 

17.38 

0.37 

IT.T:. 

•."- 

17- 

l-l    : 

9.71 

963 

•J.M 

384.93 

9.78 

197.78 

6.39 
0.45 

0.39 

i 

9.90 

3.58 

C.5I 

•.'II 
819 
818 

IT 

1:1      '-M 

816.74 
819.16 

'•'<•  '.-.' 

-3.00 
3.09 
3.19 
3.98 

1.48 
Ml 

•  - 

0.83 

9.91 

0.80 

10.71 

966 

889 
861 

399.79 
396.09 

899.48 
4014H 
403.44 
106.98 

-  •>.  i; 
Ml 

3.14 
9.04 
1.93 
1.81 
1.69 

II  t.--> 
108:96 

I'M.  i.l 

94.97 
98.96 
81.48 
:  1.66 

Ml 

6.77 
6.83 
6.86 
6.91 

18.07 

0.38 

is.:!.-, 

0.33 

18.581 

0.17 

Ml 

n.  I- 

884 

1.58 

68.94 

6.95 

18.76 

5.41 

i 

0.75 

1.46 

.    n 

8M 

.-.•-. 

71 

-••"" 

• 

•  .-  i    17 

-3.93 
4.03 
4.11 

H.'.'l 
-4.99 

-0.79 

-19.95 

888 

•,v.r, 

970 

419.56 
118.66 
414.64 

-II.  -,.:,  I 

-  1.35 
1.93 
1.11 
0.98 
-0.87 

f  iii.'.i:, 
39.93 

18.66 
+  11.51 

o.w 

-7.09 
7.06 
7.09 

-7.15 

0.19 

i-  -; 

-0.07 

17 


KUlfiyEHsiTyj 

TABLE    IV.—  Continued.              ^^FJ^^^ 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

Terms  multiplied  with  t.     Argument  =  M. 

Arg. 

cl 

Diff. 

'/ 

Diff. 

P 

Diff. 

Arg. 

tt 

•3 

Diff. 

'/ 

Diff. 

?          Diff. 

o 

0 

270 

-415.51 

+  11.51 

-  18.94 

315 

-318.07 

-303.11 

-  13.83 

271 

416.25 

-  0.74 

+    4.33 

-7.18 

-0.02 

316 

313.53 

+  5.14 

309.00 

-5.89 

+  0.72 

0.61 

7.21 

5.26 

5.81 

272 

416.86 

-    2.88 

317 

308.27 

314.81 

273 

417.34 

0.48 

10.11 

7.23 

18.90 

318 

302.89 

5.38 

320.52 

5.71 

13.11 

274 

417.70 

0.36 

17.36 

7.25 

+  0.03 

319 

297.40 

5.49 

320.13 

5.61 

0.76 

275 

417.94 

0.24 

24.63 

7.27 

320 

291.80 

5.60 

331.65 

5.52 

—  0.10 

7.29 

5.71 

5.41 

276 

418.04 

31.92 

18.93 

321 

280.09 

337.06 

12.35 

277 

418.02 

+  0.02 

39.22 

.    7.30 

0.08. 

322 

280.27 

5.S2 

342.37 

5.31 

0.80 

0.16 

7.32 

5.93 

5.21 

278 

417.86 

46.54 

323 

274.34 

347.58 

0.28 

7.33 

6.03 

5.10 

279 

417.58 

53.87 

18.85 

324 

268.31 

352.68 

11.55 

0.42 

7.33 

6.13 

4.98 

280 

^417.16 

-  61.20 

0.14 

325 

-202.18 

-357.66 

0.83 

281 

416.62 

+  0.54 

68.54 

-7.34 

326 

255.94 

+  6.24 

302.54 

—  4.88 

0.68 

7.35 

6.34 

4.76 

282 

415.94 

75.89 

18.71 

327 

249.00 

367.30 

10.72 

283 

415.13 

0.81 

83.23 

7.34 

328 

243.17 

6.43 

371.94 

4.64 

0.87 

284 

414.19 

0.94 

90.58 

7.35 

0.19 

329 

236.64 

6.53 

370.47 

4.53 

.08 

7.33 

6.63 

4.41 

285 

413.11 

97.91 

18.52 

330 

230.01 

380.88 

9.85 

.21 

7.32 

6.72 

4.28 

286 

411.90 

105.23 

m 

331 

223.29 

385.16 

0.90 

.35 

7.33 

6.81 

4.15 

287 

410.55 

112.56 

0.95 

332 

216.48 

389.31 

.48 

7.31 

I 

6.88 

4.02 

288 

409.07 

119.87 

18.27 

333 

209.60 

393.33 

8.95 

289 

407.45 

.62 

127.16 

7.29 

334 

202.03 

6.97 

397.22 

3.89 

1.75 

7.28 

0.29 

7,05 

3.77 

0.92 

290 

-405.70 

-134.44 

335 

-195.58 

-400.99 

291 

403.81 

+  1.89 

141.70 

-7.26 

17.98 

336 

188.40 

+  7.12 

404.02 

-  3.63 

8.03 

292 

401.79 

2.02 

148.94 

7.24 

0.35 

337  • 

181.20 

7.20 

408.11 

3.49 

0.95 

2.15 

7.2*2 

7.27 

3.36 

293 

399.64 

156.16 

338 

173.99 

411.47 

294 

397.35 

2.29 

163.34       7'  8 

17.03 

339 

106.65 

7.34 

414.08 

3.21 

7.08 

235 

394.93 

2.42 

170.49        ™5 

0.40 

340 

159.25 

6.40 

417.75 

3.07 

0.97 

296 

392.37 

2.56 

177.62 

341 

151.78 

7.47 

420.09 

2.94 

297 

389.07 

2.70 

184.71 

17.23 

342 

144.24 

7.54 

'  423.48 

2.79 

0.11 

298 

386.84 

2.83 

191.76        I'"5 

•1 

343 

136.65 

7.59 

426.12       S'64 

0.99    i 

299 

383.88 

2.96 

198.77        ''OI 

0.45 

344 

129.00 

7.65 

428.62 

2.50 

;          3.09 

C.97 

7.63 

2.36 

300 

-380.79 

-205.74 

16.78 

I!!') 

-121.31 

-430.98 

5.12 

301 

377.56 

+  3.23 

212.66    ~6'92 

0.50 

340 

113.58    +  7'73 

O  Ol 

433.19 

1.00 

3.37 

fi  87 

7  7ft 

on, 

302- 

374.19 

o   rA 

219.53 

. 

347 

105.80 

435.24        "" 

303 

370.69 

J.OU 

220.35       8~* 

10.28 

348 

97.97        7'83 

437.14        1-90 

4.18 

304 

367.06 

3.63 

233.11 

0.54 

349 

90.11        7-SG 

438.89 

1.75 

1.02 

305 

303.30 

3.76 

239.81 

350 

82.21       7'9° 

440.49 

1.60 

300 

359.41 

3.89 

240.40        °'6J 

15.74 

351 

74.28  ,      ''93 

441.93        M' 

4.02 

fi  r>8 

-     Qfi 

307 

355.39 

253.04        6'"8 

0.59 

353 

66.32  i      "96 

443.22  i      Ka9 

1.03 

308 

351.21 

4.15 

259.55        6"r>1 

353 

-  qo 

58.33 

444.:;,;      lAgl 

309 

346.90        *'" 

200.00  i     C-45 

15.15 

354 

50.33        8'00 

2.07 

4.40 

6.37 

8.02 

0.82 

310 

-342.50  ; 

-272.37  ; 

0.64 

355 

-  42.31 

-446.18 

1.03 

311 

338.03  i  + 

278.08  i  ~  6'31 

350 

34.27  ;  +  S'°4 

440.83     -°'C7 

312 

333.38  !     *'" 

284.91 

11.51 

357 

26.21  i      8'°6 

447.31 

1.0-1 

313 

328.00!     4''8 

1       Ml 

291.00  j     6'15 

+  0.68 

358 

18.15 

447.09  i 

+  1.04 

314 

323.69 

297.13        B'°7 

359 

10.08  i      8'°? 

447.89        °'2° 

315 

-318.67 

+  5.02 

-303.11 

-  13.83 

300 

-    2.01 

-447.93    -0'04 

0.00   i 

II- 


18 


TABLE    IV  .—Continued. 

I'KHTI  KI'.ATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  I. 

Ar,. 

«' 

Diff 

«• 

nr. 

C1 

Diff. 

Arg. 

f 

Diff. 

•/ 

Diff. 

f 

Diff. 

o 

o 

0 

1 

-  7 

+10 

+  n 

45 
46 

+603 

etc 

+13 

+  74 
63 

-is 

+  10 

8 

us 

5 

1 

47 

089 

13 

48 

14 

3 

214 

43 

10 

11 

48  • 

649 

13 

34 

14 

10 

4 

210 

33 

,0 

49 

i  .1 

13 

19 

15 

881 

11 

50 

665 

11 

+    3 

16 

0 

1   . 

V 

U 

10 

11 

51 

678 

11 

-  14 

17 

10 

7 

1  i 

1 

-    1 

11 

52 

687 

11 

31 

17 

8 

203 

—  1 

+  10 

11 

53 

G97 

10 

49 

18 

9 

804 

+  1 

20 

n 

54 

706 

9 

67 

18 

10 

1 

n 

8 

19 

10 

+205 

+  31 

66 

+714 

+  86 

11 

207 

•f  a 

41 

+10 

56 

728 

+  8 

106 

-20 

U 

310 

3 

68 

11 

11 

57 

729 

7 

126 

20 

10 

13 

213 

3 

n 

10 

58 

735 

6 

147 

21 

14 

BU 

I 

78 

10 

59 

740 

5 

168 

15 

223 

1 

81 

9 

10 

60 

7-ir> 

5 

189 

21 

10 

16 

0 

91 

10 

61 

74'J 

4 

211 

22 

17 

•.'  :•  . 

7 

100 

9 

62 

768 

3 

233 

23 

1- 

244 

8 

lu- 

8 

10 

63 

7.M 

2 

856 

23 

10 

19 

888 

8 

ll! 

8 

64 

755 

+  1 

278 

22 

9 

7 

0 

23 

30 

+261 

+123 

65 

+7.V> 

-301 

21 

271 

130 

+  7 

10 

66 

7.M 

-  1 

384 

-23 

9 

22 

381 

10 

137 

7 

67 

753 

1 

348 

94 

33 

.,   ,.: 

11 

143 

C 

68 

750 

3 

23 

24 

:•.   '. 

1  1 

148 

& 

10 

69 

74G 

4 

804 

2:1 

9 

88 

Hf 

188 

4   • 

70 

7  I'.' 

4 

417 

23 

26 

328 

13 
13 

186 

4 

71 

737 

5 

111 

24 

37 

::  1  1 

159 

3 

10 

72 

731 

6 

23 

8 

•-'- 

•• 

162 

3 

73  ' 

7-.M 

7 

y  -    23 

•." 

::•  - 

11 

161 

1 

71 

716 

8 

510          » 

M 

+  1 

9 

22 

30 

31 

•  08 
396 

+  H 
IP 

+164 
164 

0 

11 

7.-, 
76 

+707 
G97 

-10 

-5H3 
566 

-S3 

8 

32 

411 

i.i 

u 

—  1 

.77 

687 

10 

r.77 

22 

168 

1 

11 

78 

676 

11 

609 

... 

7 

3 

663 

13 

21 

4.V, 

i 

3 

90 

650 

13 

en 

H 

16 

4 

11 

81 

14 

668 

21 

7 

37 

i  •, 

147 

-.• 

14 

20 

'- 

i  - 

Ml 

6 

83 

GOG 

M 

702 

90 

• 

1  .1 

7 

10 

84 

590 

16 

7'JI 

10 

6 

15 

M 

17« 

19 

40 

+  1  •„•<•, 

-t  :,7:t 

-711) 

41 

|  * 

117 

—  9 

fkV. 

-17 

-18 

I  ; 

9 
in 

10 

87 

18 

77T, 

17 

f, 

14 

•- 

lo 

88 

519 

:  i 

709 

17 

44 

45 

-.'' 

H 
+  74 

-U 

+  10 

89 
90 

500 

*  l-i 

It 
-90 

808 
-.'1 

16 
-16 

+  5 

19 


TABLE    IV.  —  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS 

OF  THE  SIXTH  DECIMAL. 

ARGUMENT  I. 

Arg. 

el 

Diff. 

,/ 

Diff. 

f    ' 

Diff. 

Arg. 

f 

Diff. 

5' 

Diff. 

£' 

Diff. 

o 

0 

90 
91 

+480 
460 

-20 

-824 
838 

-14 

+  5 

135 
136 

-484 
499 

-15 

-782 
769 

+13 

-7 

21 

14 

]4 

13 

92 

439 

852 

137 

513 

ia 

756 

11 

93 

418 

21 

866 

14 

4 

138 

526 

lo 

743 

Jo 

8 

22 

13 

13 

14 

94 

396 

879 

139 

539 

729 

oo 

12 

13 

14 

95 

374 

891 

140 

552 

715 

96 

351 

23 

902 

11 

3 

141 

564 

12 

702 

13 

<) 

23 

10 

11 

14 

97 

328 

912 

142 

575 

688 

98 

305 

23 

921 

9 

143 

586 

11 

674 

14 

23 

j  [ 

14 

99 

282 

930 

3 

144 

597 

660 

9 

24 

8 

10 

14 

100 
101 

+258 
234 

-24 

-938 
945 

-  7 

145 
146 

-607 
617 

-10 

-646 
C32 

+14 

102 

210 

24 

952 

7 

2 

147 

626 

9 

618 

14 

10 

103 

186 

24 

957 

5 

148 

635 

9 

604 

14 

24 

5 

9 

14 

104 

162 

962 

149 

644 

590 

24 

4 

g 

14 

105 

138 

966 

+  1 

150 

C52 

576 

10 

24 

3 

Q 

14 

106 

114 

969 

151 

660 

562 

25 

3 

7 

14 

107 

89 

972 

152 

667 

5-48 

24 

i 

7 

14 

108 

65 

973 

* 

0 

153 

674 

534 

11 

109 

41 

24 

974 

-  1 

154 

681 

7 

•520 

14 

24 

0 

7 

13 

110 

+  17 

-974 

155 

-688 

-507 

—  24 

Q 

—  6 

+14 

111 

-    7 

974 

-1 

156 

694 

493 

12 

24 

+    1 

6 

13 

112 

31 

973 

157 

700 

480 

23 

2 

g 

14 

113 

54 

971 

158 

706 

466 

114 

77 

23 

968 

3 

1 

159 

711 

5 

453 

13 

12 

115 

100 

23 

964 

4 

160 

716 

5 

440 

13 

116 

123 

23 

960 

4 

161 

721 

5 

427 

13 

117 

146 

23 

955 

5 

1C2 

72G 

5 

414 

13 

13 

118 

168 

950 

5 

2 

163 

730 

4 

401 

13 

22 

g 

4 

12 

119 

190 

944 

161 

734 

389 

22 

7 

5 

13 

120 

-212 

-937 

3 

165 

-739 

-376 

13 

121 

233       " 

930 

+  7 

166 

743 

:     ~  4 

364 

+12 

122 

254 

922 

8 

167 

746 

3 

352 

12 

123 

.      274 

914 

8 

4 

168 

750 

* 

340 

12 

J3 

124 

294 

~u 

905 

9 

169 

754 

4 

328 

12 

125 

314 

20 

896 

9 

170 

758 

4 

316 

12 

19 

10 

Q 

12 

126 

333 

886 

5 

171 

761 

304 

14 

19 

in 

Q 

12 

127 

352 

876 

i 

172 

764 

292 

128 

370 

18 

865 

11 

173 

768 

4 

280 

12 

129 

388 

854 

11 

6 

174 

771 

3 

269 

11 

14 

17 

11 

3 

12 

130 

-405 

-843 

. 

175 

-774 

-257 

131 

422 

—  17 

831 

+12 

176 

778 

-4 

246 

+11 

132 

438 

1U 

819 

12 

6 

177 

781 

3 

234 

12 

14 

133 

454 

If 

807 

12 

178 

784 

3 

223 

11 

134 

469 

15 

795 

12 

179 

787 

3 

212 

11 

135 

-484 

-  15 

-782 

+13 

-7 

180 

-790 

-3 

-200 

+12 

-14 

20 


TABLE    I  V.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  I. 

Ar«. 

f 

Diff. 

¥ 

Diff. 

f 

Diff. 

Arg. 

f 

Diff. 

* 

Diff. 

c* 

Diff. 

e 

o 

1-  • 

181 

-790 
7U3 

-3 

-200 

i-  > 

+11 

-14 

225 

HI 

-839 

-  .;.: 

+  6 

+466 

484 

+19 

-13 

M 

796 

3 

178 

ll 

H7 

6 

504 

90 

183 

799 

3 

166 

13 

15 

Ml 

820 

7 

524 

90 

13 

184 

3 

IM 

11 

m 

812 

8 

20 

Iff 

805 

3 

143 

19 

230 

804 

8 

564 

90 

\-\ 

4 

132 

11 

U 

',':il 

795 

9 

584 

20 

12 

187 

Ml 

3 

120 

19 

:>:« 

786 

9 

604 

90 

I-- 

815 

3 

109 

11 

233 

776 

10 

19 

189 

818 

3 

97 

19 

15 

IM 

765 

11 

643 

90 

12 

3 

19 

11 

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190 
191 

--.'I 

M 

-3 

-  85 
73 

+19 

235 
236 

-754 
742 

+12 

+663 
683 

+20 

r.»2 

-J7 

3 

Cl 

19 

15 

237 

729 

13 

702 

19 

n 

193 

830 

49 

19 

238 

716 

13 

rai 

20 

194 

633 

36 

13 

239 

702 

14 

741 

19 

3 

24 

19 

15 

240 

687 

IS 

760 

19 

10 

196 

-  :  i 

-  11 

13 

Ml 

672 

15 

779 

19 

197 

842 

3 

+    2 

13 

242 

G5G 

16 

797 

18 

198 

Mi 

3 

16 

14 

15 

Ml 

17 

815 

,8 

10 

199 

847 

89 

•Jii 

V» 

17 

833 

18 

3 

14 

18 

18 

200 
201 

Ml 
•j  i 

-850 
Ml 
MI 

-,.., 

-3 

9 
3 
9 

+  43 
57 
71 

+14 
14 
14 
14 

15 
15 

245 

Ml 

•JI7 

Ml 

Ml 

-604 
585 
565 
545 
Ml 

+19 
90 
90 
90 

+851 
863 
-1 
900 
916 

+17 
16 
16 
16 

9 

a 

M 

IM 

503 

99 

:i:u 

15. 

1  : 

-.., 

-J 

1 

130   ; 

145           '* 
161 

15 

Ml 

m 

481 

459 
4:!0 

99 
93 

946 
960 

15 
14 
13 

7 

-    • 

-  : 

177 

•.-.-.I 

412 

94 

n 

210 

211 

-,  , 

1 
-1 

1C 

;    +'• 

15 

Ml 

-388 

303 

94 

fin-* 

lllll'.l 

is 

+  19 

6 

212 

-,,, 

9i 

1019 

10 

-.,, 

U 

Ml 

96 

in-.".) 

10 

5  • 

•.•II 

-.' 

41 

•  • 

HI 

• 

1036 

9 

-  : 

1 
1 

Ml 

14 

M  ' 

m 

97 
97 

1040 

8 

7 

4 

'.'17 

Ml 

97 

7 

-  i 

i 

•tii         " 

178 

27 

1000 

HIM;            " 

19 

14 

•,-t.i 

150 

• 

1071 

3 

3 

It 

M 

n 

M 

-••j 

-,. 
Ml 

43 

4 
4 

.  M 

1* 

. 

14 

M 
Ml 

-122 

M 

+99 

+  1(174 
1(177 
I07H 

3 

+    3 
9 

2 

M 

-i- 
-ii 

4 
44 

Iff 

.       .    , 

.-    8 

..., 

ton 

1081 

—  1  — 



.  !•    . 

-^^—  _^^____ 

- 

-13 

270 

+  21 

+99 

-    1 

-  1 

21 


TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  I. 

Arg. 

b 

Diff. 

,/ 

Diff. 

f 

Diff. 

Arg. 

f 

Diff. 

,/ 

Diff. 

* 

Diff. 

\ 

O 

o 

270 

+  31 

+1080 

-  1 

315 

+778 

+259 

+10 

271 

50         +3U 

io/a 

-  2 

316 

"   774 

—  4 

235 

-24 

29 

3 

5 

23 

272 

79 

1075 

317 

769 

212 

273 

107 

28 

1071 

4 

0 

318 

764 

5 

189 

23 

10 

29 

5 

7 

23 

274 

136 

1066 

319 

757 

166 

28 

5 

7 

22 

275 

164 

1061 

320 

750 

144 

29 

7 

g 

21 

276 

193 

1054 

+  1 

321 

742 

123 

10 

28 

g 

g 

SI 

277 

221 

1046 

322 

733 

102 

28 

10 

20 

278 

249 

1038 

' 

323 

723 

82 

27 

10 

10 

19 

279 

276 

1028 

2 

324 

713 

63 

11 

27 

11 

11 

19 

280 

+303 

+1017 

325 

+702 

$•  44 

281 

330 

+27 

1006 

-11 

326 

690 

-12 

26 

-18 

26 

]3 

12 

17 

282 

356 

-993 

3 

327 

678 

+    9 

11 

26 

13 

13 

16 

283 

382 

980 

328 

665 

-    7 

25 

14 

14 

16 

284 

407 

966 

329 

651 

23 

25 

15 

14 

14 

285 

432 

951 

4 

330 

637 

37 

11 

24 

16 

14 

14 

286 

456 

935 

331 

623 

51 

24 

17 

15 

13 

287 

480 

918 

332 

608 

64 

23 

18 

15 

12 

288 

503 

900 

4 

333 

593 

76 

11 

OQ 

18 

15 

11 

289 

525 

882 

334 

578 

87 

21 

19 

16 

10 

290 

+546 

+  863 

335 

+562 

-  97 

291 

567 

+21 

843 

-20 

5 

336 

547 

—15 

106 

—  9 

11 

20 

21 

16 

g 

292 

587 

822 

337 

531 

114 

19 

21 

16 

8 

293 

606 

801 

338 

515 

122 

18 

22 

16 

6 

294 

624 

779 

6 

339 

499 

128 

11 

17 

22 

16 

6 

295 

641 

757 

340 

483 

134 

17 

23 

16 

4 

296 

658 

734 

341 

467 

138 

15 

23 

16 

4 

2i>7 

673 

711 

7 

342 

451 

142 

11 

* 

14 

24 

16 

3 

298 

687 

687 

343 

435 

145 

299 

701 

14 

663 

24 

344 

419 

16 

146 

1 

13 

24 

15 

-  1 

300 

+714 

+639 

.    ,  7 

345 

+404 

+147 

11 

301 

725 

+  11 

614- 

-25 

.    346 

389 

-15 

147 

0 

11 

26 

15 

+  1 

302 

736 

588 

347 

374 

146 

303 

745 

9 

g 

563 

25 
25 

8 

348 

360 

14 
14 

145 

1 
3 

11 

304 

753 

538 

349 

346 

142 

305 

761 

8 

512 

20 

350 

333 

13 

139 

3 

c 

26 

13 

4 

306 

767     j 

486 

9 

351 

320 

135 

11 

307 

772 

5 
5 

460 

26 
25 

352 

307 

13 
12 

130 

5 
5 

308 

777 

435 

353 

295 

125 

309 

780 

3 

409 

26 

9 

354 

284 

11 

119 

6 

11 

2 

25 

11 

7 

310 
311 

+782 
783 

.+  1 

+384 
35S 

-26 

355 
356 

+273 
263 

-10 

-112 
105 

+  7 

312 

783 

0 

.     333 

25 

10 

357 

254 

9 

98 

11 

313 

783 

0 

308 

25 

358 

246 

8 

90 

8 

314 

781 

-  2 

283 

25 

359 

238 

8 

81 

9 

315 

+778 

-  3 

+259 

-24 

+10 

360 

+231 

—  7 

-  72 

+  9 

+u 

22 


TABLE 

I  V  .  —  Co  n  tinned. 

PERTURBATIONS  OF 

THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

AR(.i  Mi:vr  n. 

Arg 

f 

Diff. 

Diff. 

P 

Diff. 

Arg. 

Diff 

n' 

Diff 

C 

Diff. 

o 

o 

0 
1 

-••" 
856 

-« 

-360 
344 

+18 

+39 

45 
46 

-850 
844 

+   6 

+397 
413 

+16 

+26 

B 

-   .- 

8 

337 

17 

47 

837 

7 

428 

H 

1 

868 

0 

311 

18 

29 

48 

830 

7 

4-12 

14 

M 

4 

873 

5 

BM 

17 

49 

823 

7 

457 

15 

5 

878 

A 

V77 

17 

50 

815 

8 

•471 

14 

6 

5 

MO 

17 

30 

r.i 

808 

7 

486 

15 

7 

887 

•Jl:l 

17 

800 

8 

500 

14 

8 

891 

4 

MO 

17 

53 

791 

9 

ol-l 

14 

1 

4 

309 

17 

30 

M 

783 

8 

13 

22 

4 

17 

9 

14 

10 
11 

903 

-Ul 

17:, 

+17 

55 
50 

-77-1 
703 

+   9 

+541 

+13 

u 

13 

906 
909 

• 

3 

158 
140 

17 

18 

31 

57 

58 

750 
747 

9 
9 

507 
580 

13 
13 

21 

14 

911 

133 

17 

59 

737 

10 

603 

13 

II 

16 

913 
915 

• 

105 

88 

18 
17 

31 

GO 
01 

7  -.'7 
717 

10 

10 

605 
017 

13 
13 

19 

17 

917 

. 

71 

17 

* 

02 

•      707 

10 

13 

18 
19 

930 

i 

53 

30 

18 
17 

31 

63 
04 

686 

10 

11 

041 

an 

13 
11 

18 

80 

n 

23 
34 

+931 
931 
BM 

i 

0 

-1 

0 

+1 

0 

-  J8 

-     1 
+  16 

•  j 

68 

18 

+17 
17 
18 
17 
17 

31 
31 

M 
M 

n 

-G75 
664 

an 

641 

629 
617 

11 

+11 
11 

13 
13 
13 

+063 

C7I 

086 

706 

11 

+11 
11 
11 
10 
10 

1C 
1C 

• 
•     87 

21 

MB 
BIB 

1 
1 

86    1 

120 
1:17 

18 

17 
17 

30 

71 

7:: 
74 

:.-! 
BM 

13 
19 
13 
13 

796 

7ir, 

754 

10 
9 
10 
9 

13 

1 

17 

30 

-Ml 

+  IM 

0.   - 

... 

13 

.- 

: 
34 

BM 

:".-. 
••   .• 

+8 
3 
3 
1 

171 

IM 
MB 

+17 
17 
17 
17 

39 

• 

M 

7  - 

BM 
BU 

+  13 
13 
U 

13 

771 

7-7 

+  9 
8 
8 

12 
10 

. 
I 

-., 

... 

18 

-  ) 

i-  i 

14 
14 

796 

; 

37 

4 

18 

' 

•-  1 

•17.> 

J4 

- 

6 

16 

M 

Ml 

BIO 

• 

' 

1 

18 
16 

-i 

-117 

CM 

M 
14 

7 
6 

7 

40 

-:- 

+'iri 

14 

6 

41 
43 
43 

-,.- 

+5 
i 
1 

n 

:u,7 

16 
16 

27 

87 

-419 

405 

BM 

+14 

U 
II 

.-n 

-17 

+  6 
6 

" 

* 

M 

11 

:i7.i 

14 

j 

43 

_ 

+96      > 

. 

- 

*•'  1 

1 

414 

'-I.I 

+  4 

+  4 

23 


TABLE    IN.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  II. 

Arg. 

' 

Diff. 

I1 

Diff. 

* 

Diff. 

Arg. 

f 

Diff. 

i' 

Diff. 

* 

Diff. 

O 

O 

90 

-346 

+861 

+  4 

135 

+356 

+802 

-12 

91 

331 

+15 

866 

+5 

136 

371 

+15 

795 

+  7 

15 

4 

14 

7 

92 

316 

870 

137 

385 

788 

15 

4 

14 

7 

93 

301 

874 

2 

138 

399 

781 

13 

94 

285 

16 

878 

4 

139 

414 

15 

774 

7 

15 

3 

14 

g 

95 

270 

881 

140 

428 

766 

15 

3 

14 

g 

96 

255 

884 

+  1 

141 

442 

758 

14 

97 

239 

16 

887 

3 

• 

142 

456 

14 

750 

8 

15 

2 

13 

g 

98 

224 

889 

143 

469 

742 

1A 

2 

14 

g 

99 

208 

891 

-  1 

144 

483 

734 

U 

16 

2 

13 

9 

100 

-192 

+893 

145 

+496 

+725 

101 

177 

+15 

895 

+2 

146 

510 

+14 

717 

-  8 

16 

2 

13 

9 

102 

161 

897 

2 

147 

523 

708 

14 

103 

145 

16 

898 

1 

148 

536 

13 

699 

9 

IG 

1 

12 

10 

104 

129 

899 

• 

149 

548 

689 

16 

a 

13 

9 

105 

113 

899 

3 

150 

561 

680 

15 

106 

97 

16 

900 

+1 

151 

573 

12 

670 

10 

1  R 

o 

13 

9 

107 

81 

JO 

900 

152 

586 

661 

15 

—  i 

12 

10 

108 

66 

899 

4 

153 

598 

651 

15 

16 

o 

12 

10 

109 

50 

899 

154 

610 

641 

16 

l 

12 

11 

110 

-  34 

898 

155 

+622 

+630 

111 

18 

+16 

897 

-i 

6 

156 

633 

+11 

620 

-10 

16 

16 

i 

11 

11 

112 

-    2 

896 

157 

644 

609 

16 

i 

12 

10 

113 

+  14 

895 

158 

656 

599 

16 

2 

11 

11 

114 

30 

893 

7 

159 

667 

588 

16 

16 

O 

10 

11 

i  15 

46 

891 

160 

677 

577 

110 

62 

16 

889 

2 

161 

688 

11 

565 

12 

16 

3 

10 

11 

117 

78 

886 

8 

162 

698 

554 

16 

16 

2 

10 

11 

118 

94. 

884 

163 

708 

543 

16 

3 

10 

12 

119 

110 

881 

164 

718 

531 

16 

3 

10 

12 

120 

+126 

+878 

9 

165 

+728 

+519 

16 

121 

142 

+  16 

874 

-4 

.166 

737 

+  9 

508 

—11 

122 

157 

15 

871 

3 

107 

746 

9 

496 

12 

123 

173 

16 

867 

4 

9 

168 

755 

9 

484 

12 

17 

124 

189 

16 

863 

4 

169 

764 

9 

471 

13 

185 

204 

15 

858 

5 

170 

77'3 

9 

459 

12 

126 

330 

16 

854 

4 

10 

171 

781 

8 

447 

12 

17 

127 

235 

15 

849 

5 

172 

789 

8 

434 

13 

128 

251 

16 

844 

173 

797 

8 

422 

12 

139 

266 

15 

838 

11 

174 

804 

7 

409 

13 

17 

15 

5 

8 

13 

130 

+281 

+833     ; 

175 

+812 

+396 

131 

296 

+15 

827 

-6 

176 

819 

+  7 

383 

—13 

132 

311 

15 

821 

6 

12 

177 

826 

7 

370 

13 

17 

133 

326 

15 

815 

6 

178 

832 

6 

357 

13 

134 

341 

15 

809 

6 

179 

838 

6 

343 

14 

135 

+356 

+15 

+802 

—7 

-12 

180 

+844 

+  6 

+330 

—13 

-17 

24 


TABLE    IV.—  Continued. 

PERTl  KliATIONS  OF 

TIIF.  CO-ORDINATES  IX  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  II. 

Ar, 

. 

Diff 

<' 

Diff. 

9        Diff. 

Arg. 

t 

Diff. 

Diir. 

i'           Dill". 

180 

+844 

-1-330 

-17 

o 

-i  • 

-•!!-, 

-20 

181 

850 

+6 

31G 

—14 

996 

833 

—  7 

-14 

Ifl9 

0 

13 

997 

B97 

6 

343 

14 

861 

6 

14 

1- 

99B 

820 

7 

14 

20 

184 

999 

813 

7 

871 

14 

186 

14 

230 

800 

7 

14 

875 

14 

18 

931 

790 

7 

899 

14 

90 

1-7 

23g 

791 

8 

413 

14 

188 

884 

4 

H 

14 

933 

8 

42G 

13 

189 

-•r 

j 

1- 

234 

77:, 

8 

440 

14 

20 

4 

14 

9 

13 

190 
191 

+891 
894 

+3 

4-199 

17- 

-14 

+798 

758 

-  8 

-463 

4G7 

-14 

-  'T 

|64 

18 

237 

749 

480 

90 

193 

899 

149 

938 

740 

9 

493 

13 

194 

136 

930 

731 

9 

50G 

994 

ttl 

I- 

240 

721 

10 

519 

13 

20 

196 

.I, 

Mr, 

941 

712 

9 

539 

13 

907 

242 

70-2 

10 

12 

.VI  1 

1  - 

|  - 

19 

243 

699 

10 

557 

90 

199 

,,, 

63 

944 

11 

11 

..,,, 
M 

+910 
910 
911 

1 

0 

-fl 

34 

n 

li 

-14 
15 

19 

946 
946 

247 

+G71 
GGO 
649 

10 

-11 
11 

-581 
593 
606 

13 

-n 

19 

•.'  •  : 

1111     ; 

+     4 

1  1 

94S 

11 

617 

'.'  •! 

906 

1  : 

•j    • 

.,., 

m 

i 

904 

1 

1 
1 

-  10 
54 

14 
14 

I'.i 

in 

949 

•-''.I 
969 
953 

11 
616 

i;o:i 

11 

• 

,3 

640 

663 
674 

('•-:, 

n 

n 
n 
n 

19 
10 

-j 

15 

- 

211 

900 

-  >i 

II:! 
149 

-13 
14 
II 
II 

19 

956 

13 

.-,17 

706 
716 

7  '-'t  i 

n 

-10 
10 
10 

(8 

-  '! 

... 

4 

-    ' 

171 

186 

II 

14 

l.'p 

in 

I'M          '3 

-.77 

464 

I  1 

736 
74.i 
755 

7«;r,         10 

17 

4 

II 

'./(>.! 

11 

771 
1 

16 

m 
m 

• 

.      ' 
, 

-U 
14 

997 

14 

M 

-7:n 

- 

•1 
1 

n; 

M 

-1 

—  ^—  .^-^_ 

301 

—  ^—  ^—  ^—  ^— 

M 
-14 

-90      1 

MI  .  i 

i  -» 

BIO 

.•i 

8 

-  7 

-16 

25 


TABLE     IV  .—Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  II. 

Arg. 

f 

Diff. 

'/ 

Diff. 

f 

Diff. 

Arg. 

f 

Diff. 

»' 

Diff. 

n 

Diff. 

o 

o 

270 
271 

+351 
337 

-14 

-831 
839 

-8 

-15 

315 
316 

-346 
360 

-14 

-884 
878 

+6    • 

+  7 

272 

322 

15 

846 

7 

317 

375 

15 

872 

6 

27? 

307 

15 

853 

7 

14 

318 

390 

15 

866 

6 

9 

274 

292 

15 

859 

6 

319 

404 

14 

859 

7 

275 

277 

15 

866 

7 

320 

419 

15 

852 

7 

276 

262 

15 

872 

6 

13 

321 

433 

14 

845 

7 

10 

277 

247 

15 

877 

5 

322 

447 

14 

837 

8 

278 

234 

15 

883 

6 

323 

461 

14 

829 

8 

279 

216 

16 

888 

5 

12 

324 

475 

14 

821 

8 

12 

15 

5 

13 

8 

280 
281 

+201 
186 

-15 

-893 

898 

-5 

325 

326 

-488 
502 

-14 

-813 

804 

+9 

282 

170 

16 

903 

5 

10 

327 

516  ' 

14 

795 

9 

14 

283 

154 

16 

907 

4 

328 

529 

13 

786 

9 

284 

139 

15 

911 

4 

329 

542 

13 

776 

10 

285 

123 

16 

914 

3 

9 

330 

555 

1  1 

766 

10 
ift 

16 

286 

107 

16 

918' 

4 

331 

568 

lo 

756 

1U 

287 

92 

15 

921 

3 

332 

580 

12 

745 

11 

16 

3 

13 

10 

288 

76 

924 

8 

333 

593 

735 

17 

289 

00 

16 

926 

2 

334 

605 

12 

724 

11 

16 

2 

12 

12 

290 

+  44 

-928 

335 

-G17 

-712 

291 

28 

-16 

930 

-2 

6 

336 

629 

-12 

701 

+11 

19 

15 

12 

12 

292 

+  13 

932 

337 

641 

689 

293 

-    3 

16 

933 

1 

338 

652 

11 

677 

12 

294 

19 

16 

934 

1 

5 

339 

664 

12 

665 

12 

20 

16 

1 

11 

13 

295 

35 

935 

340 

675 

652 

296 

51 

16 

9I!5 

0 

341 

686 

11 

640 

12 

16 

10 

13 

297 

67 

935 

3 

342 

696 

627 

22 

298 

82 

15 

935 

0 

343 

707 

11 

614 

13 

16 

Q 

10 

14 

299 

98 

935 

344 

717 

600 

16 

+1 

10 

13 

300 

-114 

-934 

-  2 

345 

-727 

-587 

23 

301 

130 

-16 

933 

+1 

346 

737 

-10 

573 

+14 

16 

2 

10 

14 

302 

146 

931 

347 

747 

539 

303 

161 

15 

930 

1 

0 

348 

756 

9 

544 

15 

25 

Ifi 

2 

9 

14 

304 

177 

928 

349 

765 

530 

305 

193 

16 

925 

3 

350 

774 

9 

515 

15 

15 

Q 

9 

14 

306 

208 

923 

+  2 

351 

783 

501 

26 

307 

224 

16 

920 

3 

352 

791 

8 

486 

15 

308 

239 

15 

916 

4 

353 

799 

8 

470 

16 

309 

255 

16 

913 

3 

3 

354 

807 

8 

455 

15 

27 

15 

4 

8 

15 

310 

-270 

-909 

355 

-815 

-440 

+5 

—  g 

+16 

311 

285 

904 

356 

823 

424 

312 

301 

16 

900 

4 

5 

357 

830 

7 

408 

16 

28 

15 

5 

7 

16 

313 

316 

895 

358 

837 

392 

314 

331 

15 

890 

5 

359 

843 

6 

376 

16 

315 

-346 

-15 

+884 

+6 

+  7 

360 

-850 

-360 

+16 

+29 

H- 


26 


TABLE    IV  .—Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  III. 

Arg 

f 

Diff. 

«• 

Diff. 

C 

Diff. 

Arg. 

f 

Diff. 

*' 

Diff. 

9 

Diff. 

o 
0 

+312 

-  84 

-  2 

o 
45 

+  28 

4476 

1 

316 

'    +  4 

72 

+19 

46 

17 

-11 

-  l 

3 

19 

n 

O 

2 

319 

60 

47 

+    6 

•J7-.' 

3 

:i->-j 

3 

47 

13 

48 

-    5 

ll 

270 

2 

* 

19 

11 

3 

4 

324 

H 

49 

16 

267 

| 

5 

1 

23 

19 

50 

27 

ll 

264 

3 

-  i 

6 

HI 

1 

-  11 

19 

51 

38 

11 

261 

3 

7 

:;_•: 

+  1 

+    2 

13 

52 

48 

10 

257 

4 

0 

IS 

10 

A 

8 

'"','7 

14 

53 

58 

253 

9 

M 

—  1 

27 

13 

54 

68 

10 

248 

5 

1 

19 

9 

5 

10 

+325 

+  39 

2 

55 

-  77 

+243 

11 

HI 

•-  9 

51 

+19 

56 

87 

-10 

238 

^  5 

12 

321 

9 

63 

19 

57 

96 

9 

232 

6 

13 

318 

3 

75 

19 

58 

104 

8 

226 

6 

14 

314 

4 

87 

19 

59 

113 

7 

220 

C 

15 

311 

3 

99 

19 

GO 

It! 

8 

213 

7 

i 

16 

306 

5 

110 

11 

Gl 

128 

7 

206 

7 

17 

301 

6 

121 

11 

62 

135 

7 

199 

7 

18 

296 

132 

11 

63 

142 

7 

192 

7 

19 

290 

6 

143 

11 

64 

149 

7 

184 

8 

7 

10 

6 

7 

30 
21 

m  • 

276 

-  7 

+153 
163 

+10 

2 

H 
66 

-155 
161 

-  6 

+177 
169 

-  8 

22 

7 

173 

1 

67 

166 

5 

161 

8 

23 

261 

182 

68 

171 

& 

153 

8 

94 

253 

I'M 

69 

17G 

5 

144 

9 

H 

245 

200 

9 

70 

180 

* 

136 

8 

i 

• 

236 

208 

8 

71 

183 

3 

128 

8 

R) 

9 
10 

KM 

8 
7 

72 

187 

4 

119 

9 

H 

217 

'.'•.'  I 

73 

190 

111 

8 

H 

HI 

10 

230 

7 

74 

.    192 

9 

102 

9 

10 

6 

9 

8 

30 

—10 

MM 

2 

::. 

-I'.U 

+  ''I 

31 

187 

242 

n 

IM 

-  9 

86 

-  8 

32 

191 

10 

•Jl- 

77 

198 

9 

77 

9 

33 

166 

•.'"•  : 

78 

IM 

-  1 

GO 

8 

34 

IM 

n 

79 

IM 

0 

n 

8 

:;-, 

143 

HI 

80 

IM 

0 

8 

2 

H 

11 

HI 

81 

|T, 

0 

45 

8 

37 

121 

19 

HI 

-•j 

0 

37 

8 

• 

109 

II 

-'71 

83 

IM 

+  1 

H 

8 

39 

98 

273 

84 

191 

1 

22 

7 

19 

9 

1 

8 

40 

.   -,. 

—11 

-  1 

-;, 

-196 

+  14 

41 

*  ' 

-f, 

r.'i 

+  9 

+     7 

-  7 

42 

-7 

IM 

9 

0 

7 

43 

:.i 

»> 

i-  . 

3 

-     G 

6 

44 

40 

—19 

-'.i 

187 

9 

13 

7 

1.', 

n  I 

l-l 

+  3 

-  in 

-  6 

-  2 

27 


TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  III. 

Arg. 

f 

Diff. 

*' 

Diff. 

P 

Diff. 

Arg. 

« 

Diff. 

¥ 

Diff. 

* 

Diff. 

0 

0 

90 

-184 

-  19 

-  2 

135 

-  11 

-  59 

91 

181 

+  3 

25 

-  6 

136 

9 

+  3 

57 

+  2 

92 

177 

4 

31 

6 

137 

8 

1 

55 

a 

93 

173 

4 

37 

6 

138 

7 

l 

53 

a 

94 

170 

3 

42 

5 

139 

7 

0 

50 

3 

95 

166 

4 

47 

5 

140 

6 

l 

48 

a 

96 

162 

4 

52 

5 

141 

6 

0 

46    . 

a 

5 

5 

.f.  1 

\ 

97 

157 

57 

142 

5 

45 

0 

98 

153 

4 

61 

4 

143 

5 

0 

43 

a 

99 

149 

4 

65 

4 

144 

5 

0 

41 

a 

5 

4 

0 

a 

100 

-144 

-  69 

2 

145 

—    5 

-  39 

101 

140 

+  4 

72 

n 

146 

5 

0 

38 

+  i 

102 

135 

5 

75 

3 

147 

6 

-  1 

36 

a 

103 

130 

5 

78 

3 

148 

6 

0 

35 

i 

104 

125 

5 

81 

3 

149 

7 

1 

34 

i 

105 

120 

5 

83 

a 

150 

7 

0 

33 

i    • 

+  1 

106 

115 

5 

85 

a 

• 

151 

8 

1 

32 

i 

107 

no 

5 

87 

a 

152 

8 

0 

31 

i 

108 

105 

8 

88 

i 

153 

9 

1 

31 

0 

109 

100 

5 

90 

a 

154 

10 

I 

30 

i 

5 

i 

0 

0 

110 

-  95 

-  91 

2 

155 

-  10 

-  30 

111 

90 

+  5 

92 

—  i 

156 

11 

-  1 

29 

+  l 

112 

85 

5 

92 

0 

157 

12 

1 

29 

0 

113 

80 

5 

92 

0 

158 

13 

1 

29 

0 

114 

75 

5 

92 

0 

159 

14 

1 

30 

-  1 

115 

71 

4 

92 

0 

160 

14 

0 

30 

0 

2 

116 

66 

5 

92 

0 

161 

15 

1 

31 

1 

117 

62 

4 

91 

+  1 

162 

16 

1 

31 

0 

118 

57 

5 

91 

0 

163 

16 

0 

32 

1 

119 

53 

4 

90 

1 

164 

17 

1 

33 

1 

4 

1 

0 

1 

•    120 

-  49 

-  89 

2 

165 

-  17 

-  34 

121 

45 

+  4 

87 

+  3 

166 

18 

-  1 

35 

-  1 

122 

42 

3 

86 

1 

167 

18 

0 

36 

1 

123 

38 

4 

84 

a 

168 

18 

0 

37 

1 

124 

35 

3 

S3 

i 

169 

19 

-  t 

39 

a 

125 

32 

3 

81 

a 

170 

19 

0 

40 

i 

3 

126 

•29 

3 

79 

a 

171 

19 

0 

42 

a 

2 

2 

-f-  1 

2 

127 

27 

77 

172 

18 

44 

128 

24 

3 

75 

a 

173 

18 

0 

46 

a 

129 

22 

a 

73 

a 

174 

17 

1 

47 

i 

3 

•a 

0 

2 

. 

130 

-  19 

-  71 

-   1 

175 

-  17 

-  49 

i 

131 

17    . 

+  a 

68 

+  3 

176 

16 

+  1 

51 

-  a 

132 

15 

a 

66 

a 

177 

15 

1 

53 

a 

133- 

14 

i 

64 

a 

178 

14 

1 

55 

a 

134 

12 

a 

62 

o 

179 

13 

1 

57 

2 

135 

-  11 

+  i 

-  59 

+  3 

180 

-  12 

+  1 

-  59 

-  i 

+  4 

TABLE    IV.  —  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  III. 

Arg. 

C 

Diff. 

'/ 

Diff. 

f 

Diff. 

Arg. 

f 

Diff. 

"' 

Diff. 

f 

n,  ir. 

o 

0 

i-  • 

-  12 

-  59 

+  4 

225 

+117 

0 

181 

10 

+  a 

61 

-  a 

H6 

118 

+  i 

+    6 

+  6 

I--J 

8 

a 

63 

9 

227 

118 

0 

11 

5 

I-  : 

6 

65 

a 

228 

118 

0 

17 

6 

184 

4 

66 

v.'v!'.  i 

118 

0 

23 

G 

I-:. 

-    2 

68 

•.>:!(> 

118 

0. 

29 

6 

+  3 

i-.; 

0 

70 

•; 

231 

117 

-  1 
o 

35 

6 
6 

187 

+    2 

71 

839 

147 

41 

188 

5 

3 

73 

a 

233 

116 

1 

47 

6 

189 

7 

1 

71 

i 

234 

114 

2 

53 

6 

3 

i 

2 

G 

190 

+  10 

-  75 

5 

235 

+112 

+  59 

1  u 

.:.        +3 

76 

~~ 

236 

110 

-  2 

65 

+  6 

1  •-.- 

16 

77 

237 

108 

a 

71 

G 

193 

3 

78 

238 

106 

3 

77 

6 

UM 

3 

7:i 

239 

102 

3 

83 

6 

196 

26 

80 

240 

99 

3 

89 

G 

2 

196 

29 

o 

24'l 

95 

4 

94 

5 

197 

33 

M 

242 

n 

4 

100 

6 

198 

36 

o 

243 

87 

4 

105 

5 

199 

40     1        4 

N 

-.'II 

82 

5 

110 

5 

4 

+  i 

5 

6 

200 

+  44 

—  70 

5 

245 

+  77 

+  1  Hi 

+  3 

o 

+  5 

201 

47 

79 

246 

72 

121 

51 

78 

+  i 

247 

66 

6 

126 

5 

M 

4 

77 

1 

248 

61 

5 

130 

4 

204 

4 

76 

i 

249 

55 

6 

135 

5 

205 

74 

a 

250 

48 

7 

tag 

4 

+  1 

•M 

7'.' 

a 

251 

42 

6 

143 

4 

207 

70             « 

71 

i 

0M 

:tr, 

7 

146 

3 

n 

74 

1,1 

a 

863 

28 

" 

150 

4 

209 

77 

66 

3 

254 

21 

7 

153 

3 

4 

3 

7 

3 

-.'Hi 

+  81 

-  63 

4 

KB 

+  14 

+  l.~>ii 

•.'II 

84 

+  3 

61 

+  a 

BM 

+    7 

—  7 

UH 

+  2 

212 

-- 

4 

58 

3 

-     1 

8 

160 

a 

21.1 

91 

3 

54 

we 

8 

7 

9 

214 

94 

3 

51           \ 

16 

8 

Kilt 

i 

ni 

97 

3 

.7 

260 

24 

8 

164 

i 

0 

210 

100 

3 

43  : 

M 

32 

8 

166 

1 

217 

103 

3 

4 

._),  ,._, 

40 

8 

166 

+  i 

•Jl- 

105 

1 

4 

•.'r,:t 

1- 

8 

166 

0 

219 

108 

3 

30 

164 

8 

MB 

-  1 

1 

5 

9 

0 

M 

+110 

H 

+  4 

MB 

—  i;.i 

+  165 

111 

+  9 

21 

+  4 

168 

7:t 

-  8 

163 

—  2 

113 

1 

16 

4 

m 

81 

8 

UN 

1 

223 

111 

a 

10 

6 

- 

160 

9 

• 

m 

II'-, 

i 

—     5 

!>7 

1 

m 

9 

::• 

+117 

+  i 

0 

•.'M 

106 

-  8 

+  I.V, 

-  3 

0 

29 


TABLE    IV  .  —  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  III. 

Arg. 

*• 

Diff. 

,' 

Diff. 

f 

Diff. 

Arg. 

* 

Diff. 

r/ 

Diff. 

v 

Diff. 

270 

-105 

+155 

0 

o 

315 

-145 

-209 

271 

113 

-  8 

152 

316 

136 

+  9 

217 

-  8 

272 

121 

8 

149 

317 

127 

9 

224 

7 

273 

129 

8 

145 

318 

117 

10 

230 

6 

274 

136 

7 

141 

4 

319 

107 

10 

237 

7 

275 

144 

8 

136 

.       5 

320 

97 

10 

242 

5 

-  1 

276 

151 

7 

131 

5 

321 

87 

10 

248 

6 

277 

158 

7 

126 

5 

322 

76 

11 

253 

5 

278 

165 

7 

120 

323 

65 

11 

258 

5 

279 

172 

' 

114 

324 

53 

12 

262 

4 

6 

6 

- 

11 

3 

380 

-178 

+108 

0 

325 

-  42 

-265 

261 

184 

-  6 

101 

-  7 

326 

30 

+12 

268 

-  3 

282 

190 

C 

94 

7 

327 

18 

12 

271 

3 

283 

195 

5 

87 

7 

328 

-    6 

12 

273 

2 

384 

200 

5 

79 

8 

329 

+     6 

12 

275 

2 

285 

205 

5 

71 

8 

330 

18 

12 

276 

1 

1 

266 

209 

4 

63 

8 

;{;>( 

31 

13 

277 

-  1 

287 

213 

4 

55 

8 

332 

43 

12 

277 

0 

286 

217 

4 

46 

n 

333 

55 

12 

276 

+  ! 

289 

220 

3 

37 

9 

334 

68 

13 

275 

1 

3 

9 

12 

1 

290 

-223 

+  28 

0 

335 

+  80 

-274 

291 

226 

-  3 

18 

-10 

336 

92 

+12 

272 

+  2 

292 

228 

2 

+    9 

9 

337 

105 

13 

269 

3 

1 

10 

12 

3 

293 

229 

1 

338 

117 

.     266 

294 

230 

1 

10 

9 

339 

129 

12 

262 

4 

235 

231 

-  1 

20 

10 

340 

141 

12 

253 

4 

2 

296 

231 

0 

30 

10 

341 

152 

11 

253 

5 

297 

231 

0 

40 

10 

342 

164 

12 

248 

5 

298 

230 

+  1 

50 

10 

343 

175 

11 

242 

6 

299 

229 

1 

61 

11 

344 

186 

11 

236 

6 

2 

10 

11 

6 

300 

-227 

-  71 

-  1 

345 

+197 

-230 

301 

225 

+  2 

81 

-10 

346 

208 

+11 

223 

+  7 

3 

10 

10 

g 

302 

222 

91 

347 

218 

215 

303 

219 

3 

101 

10 

348 

227 

9 

207 

8 

304 

215 

4 

111 

10 

349 

237 

10 

198 

9 

305 

211 

4 

121 

10 

350 

246 

9 

189 

9 

2 

306 

207 

4 

131 

10 

351 

255 

9 

180 

9 

307 

202 

5 

140 

9 

352 

263 

8 

171 

9 

308 

196 

6 

150 

10 

353 

271 

8 

161 

10 

309 

190 

6 

159 

9 

354 

278 

7 

151 

10 

6 

9 

7 

11 

310 

+184 

-168 

-1 

355 

+285 

-140 

+  7 

g 

+  6 

+11 

311 

177 

177 

356 

291 

129 

312 

170 

7 

185 

8 

357 

297 

6 

118 

11 

313 

162 

8 

194 

9 

358 

302 

5 

107 

11 

314 

154 

8 

202 

8 

359 

307 

5 

95 

12 

315 

-145 

+  9 

-209 

—  7 

360 

+312 

+  5 

-  84 

+11 

-  2 

30 


TABLE    IV.—  Continued. 

PEinTUMATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  IV. 

. 

Arg. 

i'          Diff. 

•/'          Diff. 

V 

Diff. 

Arg. 

f 

Diff. 

*' 

Diff. 

{'           Diff. 

0 

o 

0 

-378 

+  4 

180 

+376 

+  85 

-  4 

5 

884 

* 

52         +33 

185 

382 

+  6 

52 

-33 

10 

887 

-  3 

-    1-            ** 

5 

190 

386 

+  4 

+  Iri 

34 

5 

15 

387 

0 

+  16 

34 

198 

386 

0 

-  ir, 

33 

91 

384 

+  3 

50 

34 

5 

200 

888 

-  3 

48 

34 

5 

96 

379 

9 

83 

33 

906 

:i77 

6 

82 

33 

30 

370 

9 

110 

33 

5 

210 

889 

8 

115 

33 

5 

35 

19 

148 

39 

916 

358 

11 

146 

31 

40 

344 

14 

179 

31 

B 

990 

844 

14 

177 

31 

r 

45 

327 

17 

lOg 

99 

986 

327 

17 

200 

29 

19 

98 

19 

28 

50 
55 

-  MM 
286 

+236 

+96 

+  4 

230 
986 

+308 

287 

-21 

960 

-26 

-4 

60 

262 

"I 

24 

4 

940 

963 

24 

984 

24 

4 

iCIO 

96 

806 

99 

946 

937 

26 

806 

• 

70 

m 

96 

327          .'! 

3 

950 

210 

27 

896 

M 

.( 

179 

• 

844 

ii 

956 

181 

• 

343 

17 

80 

85 

148 

117 

31 
31 

358 
370 

14 
19 

:! 

980 
986 

160 

118 

31 
32 

368 
360 

IS 
11 

3 

90 

84 

378 

9 

970 

86 

ft 

378 

9 

9 

H 

51 

384 

•-'7:, 

53 

33 

385 

7 

34 

+  3 

34 

—  3 

100 
105 

-  17 
+   1C 

+33 

+387 

0 

+  1 

280 
986 

+  1!) 

-34 

388 

0 

i 

110 
116 
120 
MB 

130 

50 
83 

111! 

147 

17- 

33 
33 
31 
31 

384 
878 

358 
844 

—  3 
6 
9 
11 
14 

0 
0 

-  1 

290 
906 
300 
806 

310 

18 

82 
118 

146 

177 

33 
34 
33 
31 
31 

386 
380 
871 
860 
345 

+  3 
5 
9 
II 
IS 

0 

1) 

4.  1 

IX 

140 
145 

207 
234 

97 

• 

327 

19 

998         " 

2 

816 

890 

896 

•-'(17 
936 
961 

30 
28 

H 

898 
800 
988 

17 
19 
11 

a 

150 
IM 
160 

17" 

178 

—  —  — 

01 

:r. 

. 

19 
17 
14 
18 
+  8 

236 

180 
148 

117 

.    -". 

94 

-96 

. 
• 
31 

-w 

-:i 
:t 
4 

-  4 

ii  i 

.la.'.-  •  •  --a 

886 
848 
846 

866 

880 

807 
890 
843 

880 

94 

-99 

19 
17 
15 
11 
-  9 

^rr—  =^ 

-464 

938 
910 

l-i 
150 
118 

-'. 

M 

+26 

-'- 

M 

32 

:t 
4 

+  i 

—  —  —  —  ^—  ^— 

31 


TABLE    IV  .—Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  V. 

Arg. 

f 

Diff. 

„'          Diff. 

c' 

Diff. 

Arg. 

f 

Diff. 

',' 

Diff. 

f< 

Diff. 

0 

0 

-312 

+  61 

-0 

+180 

+344 

-  74 

+  6 

5 

310 

oc      I     -26 
So     I 

185 

349 

+  5 

42 

+32 

10 

317 

+    9 

26 

6 

190 

352 

+  3 

-  10 

32 

6 

15 

317 

-  18 

27 

195 

351 

-  1 

+  22 

32 

20 

315     i 

44 

26 

6 

200 

348 

3 

54 

32 

6 

25 

310     1 

70 

26 

205 

341 

7 

86 

32 

30 

304 

95 

25 

5 

210 

331 

10 

116 

30 

5 

35 

296 

o 

120 

25 

215 

319 

12 

146 

30 

40 

285 

11 

145 

25 

5 

220 

304 

15 

174 

28 

5 

45 

273 

12 

169 

225 

286 

18 

200 

26 

14 

22 

20 

25 

50 
55 

-259 
243 

+16 

-191 
213 

-4 

230 
235 

+266 
244 

-22 

+225 
248 

+23 

+  4 

CO 

225 

18 

21 

234 

4 

240 

220 

24 

268 

20 

4 

65 

205 

20 

253 

245 

194 

26 

286 

18 

70 

183 

22 

270 

3 

250 

167 

27 

301 

15 

3 

75 

100 

23 

286 

255 

139 

28 

314 

13 

80 

130 

24 

300     i 

2 

200 

111 

28 

324 

10 

2 

85 

110 

26 

312     j 

205 

81 

30 

331 

7 

90 

83 

27 

322 

-1 

270 

51 

30 

335 

4 

+  1 

95 

55 

28 

329 

275 

+  21 

30 

337 

+  2 

28 

5 

29 

-  1 

100 

-  27     | 

-334 

0 

280 

-    8 

+336 

0 

105 

+     3 

+30 

337            3 

285 

37 

-29 

333 

-  3 

110 

33 

30 

337 

0 

+  1 

290 

65 

28 

327 

6 

-  1 

115 

62 

29 

334 

+  3 

295 

93 

28 

318 

9 

120 

92 

30 

329 

5 

2 

300 

119 

26 

308 

10 

2 

125 

121 

29 

321 

8 

305 

145 

26 

2<)5 

13 

130 

150 

29 

310 

11 

3 

310 

169 

24 

280 

15 

3 

135 

178 

28 

296 

14 

315 

191 

22 

264 

16 

140 

204 

26 

280 

16 

4 

320 

212 

21 

246 

18 

4 

145 

229 

25 

261 

19 

325 

231 

19 

227 

19 

24 

21 

17 

21 

150 

+253 

-240 

+  4 

330 

-248 

+206 

-  4 

155 

274 

+21 

216 

+24 

335 

264 

-16 

184 

-22 

160 

293 

19 

191 

25 

5 

340 

277 

13 

160 

24 

5 

105 

310 

17 

104 

27 

345 

289 

12 

137 

23 

170 

324 

14 

135 

29 

5 

350 

299 

10 

112 

25 

5 

30 

7 

25 

175 

335 

105 

355 

306 

87 

180 

+344 

+  9 

-  74 

+31 

+  6 

360 

-312 

-  6 

+  61 

-26 

-  5 

32 


TABLE    IV.  —  Continued. 
PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 
ARGUMENT  VI. 

Arg. 

r 

Diff. 

f 

Diff. 

C1 

Diff. 

Arg. 

f 

Diff. 

'/ 

Diff. 

{'           Dill'. 

e 

.       0 

+110 

+    3 

+  4 

ISII 

-114 

+    3 

-7 

5 

109 

14 

+11 

185 

114 

0 

—    (>    : 

10 

107 

9 

•Jl 

10 

4 

1'JO 

118 

+  i 

14             " 

G 

15 

105 

35 

11 

196 

ill 

a 

20 

101 

45 

10 

3 

200 

109 

a 

•j.)            9 

G 

96 

54 

9 

886 

107 

a 

40 

30 

91 

63 

3 

•Jio 

103 

4 

48 

G 

i       •k"' 

85 

TV.' 

816 

99 

4 

5C     ! 

40 

78 

80 

3 

220 

94 

M 

5 

45 

70 

87 

888 

88 

71 

8 

e 

g 

_ 

50 
55 

+  C2 
53 

-  9 

+  93 
98 

+  5 

+  2 

230 

-  82 
75 

+  7 

-  78 
84 

-5 

60 

44 

103 

+  1 

840 

68 

7 

80 

4 

65 

34 

107 

846 

CO 

e 

1C, 

70 

25 

110 

0 

250 

52 

8 

100 

8 

15 

11-' 

866 

43 

9 

mi 

80 
85 

+    5 
-    4 

113 

113 

0 

0 

200 
2G5 

M 

24 

9 
10 

!ro         » 

2 

90 

M 

14 
24 

10 

112        " 

111 

-1 

270 
876 

14 
-    4 

10 
10 

in 
in 

-  a 

0 

-  1 

100 
105 
110 
118 
120 

m 

-  33 
42 
50 
58 
66 
73 

9 

—  9 
8 
8 
8 

7 

+108 
105 

m 

96 
88 

87 

3 

-  3 
3 

4 
1 
6 

-2 
3 
4 

880 
886 

290 

300 
806 

+    G 
1C 
BB 
3C 
46 

10 

+10 
10 
10 
10 
9 

-in 

110 
108 
105 
101 
9G 

0 

+  i 
a 

3 
4 
5 

0 
0 
+  1 

130 
135 
140 
145 

80 

6 
6 
97    !        * 

81 

68 
60 

6 
7 
8 

5 

o 

810 
816 

886 

84 

72 
80 

87 

9 
8 
8 

90 
83 
/C 
68 

a 

7 

7 
8 

2 
3 

150 
155 
160 
165 

180 

— 

4 
+101 
105        -J 

110 
112 
118 

-114 

•'• 

37 
28 

20 
II 

'     :: 
===== 

7 

-  8 

0 
9 
8 
9 

-  8 

===== 

6 
6 
6 
-? 

===== 

848 

866 

SCO 

—  -     •—  •  — 

+  it:? 
98 
103 
100 
108 
110 

+110 

= 

—  —  .^—  — 

6 

+  5 
5 
3 
9 
+  9 
0 
===== 

-  59 
49 

39 

29 
19 

+    3 

— 

9 

+  10 
10 
10 
10 

11 
+11 

===== 

+  3 
3 
4 

+  4 

. 

•  • 

33 


TABLE    IV.  —  Continued. 
PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 
ARGUMENT  VII. 

Arg. 

f 

Diff. 

,' 

Diff. 

f 

Diff. 

Arg. 

f 

Diff. 

f 

Diff. 

? 

Diff. 

0 

O 

0 

+  92 

-125 

-30 

180 

-  94 

+122 

+30 

5 

93         +  ' 

10.2 

+23 

-3 

185 

95 

-  i 

99     \ 

+  3 

10 

92 

77 

25 

33 

190 

95 

0 

76 

23 

33 

0 

25 

o 

24 

15 

92 

52 

2 

195 

95 

52 

2 

20 

90 

27 

25 

35 

200 

93 

+  2 

27 

25 

35 

2 

25 

2 

25 

25 

88   ; 

-    2 

-  1 

205 

91 

+    2 

+  1 

30 

65 

+  24 

26 

36 

210 

88 

3 

-  22 

24 

36 

35 

81 

49 

25 

0, 

215 

85 

3 

47 

25 

0 

4 

25 

24 

40 

77 

74 

36 

220 

80 

71 

36 

4 

24 

5 

24 

45 

73 

98 

225 

75 

95 

5 

23 

+  1 

5 

23 

-1 

50 

+  68 

+121 

-35 

230 

-  70 

-118 

+35 

55 

62 

144 

+23 

3 

235 

64 

+  6 

141 

-23 

3 

6 

22 

21 

GO 

56 

166 

32 

240 

57 

162 

32 

7 

20 

7 

20 

65 

49 

166 

3 

245 

50 

182 

3 

70 

42 

7 

205 

29 

250 

43 

' 

201 

19 

29 

17 

g 

17 

75 

35 

222 

4 

255 

35 

218 

4 

7 

1  ^ 

g 

15 

80 

28 

237 

25 

260 

27 

233 

25 

85 

20 

8 

250 

13 

5 

265 

19 

247 

14 

5 

a 

11 

n 

10 

90 

12 

261 

20 

270 

10 

a 

259 

20 

• 

10 

g 

10 

95 

+     4 

271 

275 

-    2 

263     : 

8 

8 

6 

9 

8 

6 

100 

-    4 

+279 

-14 

280 

+    7 

-277 

+14 

105 

12 

-  8 

284 

+  5 

6 

285 

15 

+  8 

283     I 

6 

110 

20 

8 

267 

3 

8 

290 

23 

8 

287 

8 

115 

28 

8 

288 

+  ' 

6 

295 

31 

8 

289 

6 

7 

U 

J_    1 

120 

35 

287 

-  2 

300 

39 

288 

+  2 

125 

43 

8 

284 

3 

6 

305 

46 

7 

285 

3 

6 

130 

50 

7 

278 

6 

+  4 

310 

53 

' 

280 

5 

-  4 

135 

56 

6 

270 

8 

6 

315 

59 

6 

273 

7 

6 

7 

in 

Q 

n 

140 

63     1 

260 

10 

320 

65 

264 

10 

145 

69           6 

248 

12 

325 

71 

6 

253 

11 

6 

13 

6 

5 

14 

6 

150 

-  75 

+235     | 

+16 

330 

-  76     I 

-239 

-16 

(55 

so 

-  5 

220 

6 

335 

80         +4 

224 

+  15 

6 

160 

84 

4 

203 

17 

22 

340 

64 

207 

17 

22 

3 

18 

•1 

18 

1  <>."> 

87     ; 

185 

5 

345 

87 

189 

3 

170 

90 

165 

20 

27 

350 

89 

169 

20 

27 

175 

93 

3 

144 

21 

+  3 

355 

91 

148 

21 

-3 

iso 

-  1)4 

-  1 

-22 

+30 

360 

+  92 

+  1 

-125 

+23 

-30 

• 

[-1- 


34 


TABLE    IV  .—Continued. 

1T.K1  1  Ul'.AI  loNS  or  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXT  1C1MAL. 

ARGUMENT  VIII 

ARGUMENT  1\ 

Arg. 

Dill 

,'          Diff. 

ft 

Diff.         Arg. 

f 

Diff. 

,'          Diff. 

<r       Diff. 

O 

0 

0 

+206 

-  85 

_ 

0 

-  27 

-  16 

-i 

10 

217         +" 

48        ** 

10 

30 

15 

2 

20 

•-         +i 

-10          J 

20 

31 

2 

•,--'  1 

30 

31 

0 

12 

•,' 

40 

919 

40 

31 

0 

10     , 

2 

15 

• 

+  j 

3 

50 

ID7 

103 

50 

29 

7 

2 

60 

...              91 

i:.:,         » 

60 

27 

2 

5 

•i 

•'. 

QO 

A 

•1 

70 

150 

164 

70 

23 

-    2 

2 

31 

03 

4 

3 

80 

119 

187     i 

_ 

80 

19 

+  i 

9 

34 

18 

4 

90 

85 

906 

0 

90 

15 

4 

1 

37 

12 

5 

2 

100 

+'J17 

0 

100 

-  10   : 

+    6 

-1 

+  5 

+  3 

110 

+  10 

0 

110 

-    5 

9 

1 

4 

—  9 

fi 

0 

no 

-  29 

0 

120 

+   i 

11 

-1 

• 

a 

• 

• 

in 

01 

919 

0 

inn 

6 

13 

n 

.« 

U 

K 

1 

140 

103 

197 

0 

i  in 

11 

14 

0 

33 

01 

• 

1 

150 

in 

17C, 

+  1 

150 

16 

15 

+  1 

160 

164 

150 

1 

160 

21 

16 

i 

170 

188 

119 

1 

170 

,M 

16 

i 

l-i 

-» 

?   -:.       -** 

+J 

180 

+  27         +3 

+  16 

ARGUMENT  X. 

ARGUMENT  XI. 

ARGUMENT  Ml 

Arg. 

Diff. 

,/         Diff. 

Arg. 

i 

Ditr. 

v'         Diff. 

Arg. 

f       Ditr. 

,/           D.lV. 

O 

0 

o 

0 

+32 

0 

+  5 

0 

+21 

-10 

10 

6 

10 

+  1 

10 

99 

6 

20 

30 

rj 

20 

99 

-  :i 

20 

23 

-  2 

30 

38 

IT 

30 

5 

i 

7 

30 

89 

+  1 

40 

M 

21 

40 

•-••' 

11 

40 

22 

r, 

50 

50 

M 

U 

50 

21 

g 

60 

Hi 

28 

CO 

16 

IT 

60 

19 

1:1 

70 

10 

91 

70 

r.- 

19 

70 

17 

16 

80 

BO 

8 

U 

80 

14 

18 

-  1 

90 

5 

22 

N 

10 

20 

100 

-  6 

-3-.' 

100 

_ 

I 

-a 

100 

4  r. 

449 

no 

19 

30 

no 

+ 

3 

110 

+  •_' 

U 

120 

1  . 

190 

9 

•."J                               I'.'O 

-  1 

98 

in 

91 

M 

in 

n 

•Jii                     i:to 

.-, 

•>•> 

1  In 

110 

14 

18 

111) 

g 

91 

II 

180 

i 

~ 

16 

160 

19 

in 

Ml 

10 

19 

19 

100 

n; 

n; 

170 

170 

91 

[i 

ITO 

1!) 

i:i' 

+    1                                  1*0 

180 

-••1 

>  in 

1         .  tin-  Argument-.     .\*  i°  .iililr.i.  1  1-0°,  .ni.l  r.  i.-r-r  lli.-  .IRI,                      ml  ;' 

35 


TABLE    IV.—  Concluded.. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  XIII. 

ARGUMENT  XVII. 

ARGUMENT  XX. 

ARGUMENT   XXIII. 

Arg. 

P 

if 

Arg. 

? 

<f 

Arg. 

? 

1' 

Arg. 

p 

I1 

O 

O 

0 

0 

0 

-10 

-  4 

0 

_  ^ 

-  5 

0 

+  1 

0 

0 

-  1  , 

0 

20 

10 

0 

20 

4                 3 

20 

1 

0 

20 

0 

+  1 

40 

10             +  3 

40 

5 

-  1 

40 

1 

0 

40 

0 

1 

60 

8                 7 

60 

5 

+  1 

60 

1 

+  1 

60 

0 

1 

80 

5                 9                80 

5 

3 

80 

+  1 

1 

80 

0 

1 

100 

-  2                10               100 

4 

4 

100 

0 

1 

100 

+  1 

+  1 

120 

+  J                10               120 

2 

6 

120 

0 

1 

120 

1 

0 

140 

5                 9               140 

-  1 

6 

140 

0 

1 

140 

1 

0 

160 

8 

7 

160 

+  1 

6 

160 

-  1 

+  1 

160 

1 

0 

180 

+10 

+  4 

I  ISO 

+  3 

+  5 

180 

-  1 

0 

180 

+  1 

0 

ARGUMENT  XIV. 

ARGUMENT  XVIII. 

ARGUMENT  XXI. 

ARGUMENT  XXIV. 

0 

-10 

-  3 

0 

+  2 

-  ]     • 

0 

+  2 

-  2 

0 

-  1 

-  2 

20 

10 

0                20 

2 

0 

20 

2 

-  1 

20 

1 

-  1 

40 

10 

+  3                40 

2 

0 

40 

2 

o 

40 

I 

0 

60 

8 

7 

CO 

2 

+  1 

CO 

2 

+  ] 

60 

2 

0 

80 

5 

9 

80 

1 

1 

80 

2 

1 

80 

2 

+  1 

100 

-  2 

10 

100 

+  1 

2 

100 

2 

2 

100 

1 

1 

120 

+  2 

10 

120 

0 

2 

120 

+  1 

2              120 

-  1 

2 

140 

5 

9 

140 

-  1 

2 

140 

0 

2              140 

0 

2 

160 

8. 

7              160 

1 

1 

160 

-  1 

2              160 

0 

2 

180 

+10 

+  3              180 

-  2 

+  1 

180 

-  2             +2 

180 

+  1 

+  2 

ARGUMENT  XV. 

ARGUMENT  XIX. 

ARGUMENT  XXII. 

ARGUMENT   XXV. 

0 

-  2 

+15 

0 

-  1                 0 

0 

+  1 

- 

0 

0 

-  1 

20 

+  3 

15 

20 

1                 0 

20 

+  1 

20 

+ 

0 

40 

8 

13 

40 

1             -  1 

40 

0 

40 

0 

60 

12 

10 

60 

1                  1 

60 

0 

60 

0 

80 

14 

+  5                80 

0                   1 

80 

-  1 

80 

0 

100 

15 

0 

100 

0 

1 

100 

1 

- 

100 

+ 

+ 

120 

14 

-  5 

120  • 

0 

1 

120 

1 

0 

120 

0 

140 

11 

10 

140 

+  1 

1 

140 

1 

0 

140 

0 

160 

7 

13 

160 

1 

-  1 

160 

1 

0 

ICO 

0 

180 

+  3 

-15 

180 

+  1 

0 

180 

-  1 

+  1 

ISO 

0 

+ 

ARGUMENT  XVI. 

0 

-  5 

-  3 

20 

6 

-  2 

40 

6 

0 

60 

5 

+  2 

• 

80 

4 

3 

100 

-  2 

5 

120 

0 

5 

140 

+  2 

5 

160 

3 

4 

180 

+  5 

+  3 

• 

From  the  Arguments  >180°  subtract  180°,  and  reverse  the  sign  off,  rj',  and  C'- 

36 


TAP.U-:  v. 

LOGARITHMS  FOR  REFKKUINO  TIIK   PERTURBATIONS 

TO  THE 

I  (JCATOR. 

Mean  Equinox  of  the  beginning  of  the  Year. 

Year. 

eo»  (i,  x) 

coi  (y,  z) 

COB  (Z,  I) 

coi  (z,  y) 

coi  (y,  y) 

co»  (z,  y) 

cos  (z,  z) 

cog  (y,  z) 

COB  (Z,  Z) 

HUB 

9.998756 

8.151278/1 

8.870449 

8.626197 

9.963147 

9.594  !>:.« 

8.796613n 

9.596408 

.'189 

\  -:.: 

-755 

8.158664n 

8.870441 

8.628476 

9.963146 

9JS94167I 

'Hi/i 

9.696407 

9.9621!  Hi 

1858 

9.998753 

8.165956n 

8.870  l:v.' 

8.630743 

'.i.'.iinui 

:i..v>4149n 

A66n 

9.596406 

9.969196 

1859 

9.998752 

8.17309971 

8.870424 

--•998 

ii.'.M;:u43 

!i..-.'.m:n« 

-.7'M591n 

9.596404 

•.'.•.H;*JOO 

18601? 

-750 

8.180155n 

8.870415 

8.635242 

9.963141 

9.594  11  3n 

n:,;( 

9.596409 

aoa 

1861 

9.998749 

8.187069n      8.870407 

8.637474 

:i.'.«;:u4o 

:!..v.i40!ifm 

8.703-':!7/i 

9^96401 

9.962207 

ISM 

9.998747 

8.193903n 

-  -70398 

*.<;:«'JG96 

'.t.!M!3138 

:i..v.i4077» 

9.79956911 

9.596399 

9.968910 

1863 

9.996746 

8.200604n 

8.870389 

8.641905 

!».!Mi3i:i7 

9.594059n 

B.791879n 

16398 

!i.'.M;2214 

18MB 

-744 

8.207230n 

8.870380 

8.644104 

9.963135 

9.594040/j 

8.791  199n 

9.596396 

'.'.W2217 

1886 

9.998743 

8.213730n 

8.870:!7ii 

8.64i 

9.963134 

I099H 

8.7905  17n 

9.596396 

9.98999] 

1881 

9.998741 

8.220  160n 

8.8701!'.:!      H.648467 

9.9C3132 

9.594004n 

8.789835n 

9.596393 

9.969994 

1867 

9.998739 

8.22647171 

8.870354      8.650f,:i-,» 

'.'.:i(;:}i30 

MW8088H 

8.789151n 

BJ88391 

9489988 

18685 

9.998737 

8.23271  7  H 

8.870345 

8.652788 

!».!Mi31S8 

BJS89967H 

8.788466H 

9.596389 

!l.!Mi'«31 

186!) 

9.998736 

8.23884971 

8.870337 

8:654939 

!i.'.M;:ti-.'7 

9J93949H 

8.787780n 

B.596388 

1936 

1870 

9.9<>7:tl 

8.24492071 

8.870328 

8.657066 

;i.'.wi:ti2r, 

'.i.."i'.i:«i3iH 

-.7-7093H 

9.696388 

9.969938 

1871 

-732 

8.25088371 

8.870319 

8.659188 

!l.!IC,:tl23 

!i.:.!  i:t'.l|3;j 

-.7-1:40571 

9.596384 

9.989941 

I879J9 

9.998730      8.a567t;CH 

8.870310 

8.661301 

9.9C:!I'.'I 

!I..V.i:t,-!HH 

8.7857  II  :/i 

9.696389 

!i.'.Ui-J->44 

1873 

IK      8.26257071 

8.870302 

3404 

'.i.%:ui;» 

9.593^7  1;« 

-.7.-50.T.74 

9^96380 

9.969948 

1874 

9.998726      8.268321  n 

8.87(!-".':! 

•  W7 

9.'.ii;:ui7 

!i..V.I3858» 

8.784333/1 

6378 

9.969951 

1875 

-724 

-.-,'7:«i73;i      8.870284 

8.667584      9.963115 

!l..r.;t3840» 

8.78414071 

9.596376 

9.989966 

18710 

-782 

8.279r>'.i:t/i 

8.870275 

8.669661 

!I.'.M;3113 

:i.:.!i:W3in 

-,7-.".i4t;/i 

9.596374 

9.969958 

1877 

8.28510771 

8.870266 

8.671719 

;I.!M;:IIII 

!i..v.»:wo3n 

-.7  -.'•-•:.<  »7i 

9.59(i:i7i 

9.9B9969 

1878 

9.998718 

8.29056971 

8.870257 

7S7B7 

'.I.'.HKUOS 

BOS03785II 

8.7815.V./1 

!'.:.:• 

9.969966 

l-7'.i 

9718 

8.296  160n 

8.87024  •<      >.ii7.>l'.i 

;I.:H;:UO- 

•.i.r.:i:(7ii7;i 

8.78085771 

9JW888B 

9J89968 

I8B&B 

H.'.f.i-TI  1 

8.301290n 

8.870239       -.i;77-i,-^ 

:i.!»;:{|(i4 

!l..V.i:t74-;i 

8.780i:.!i« 

'.I..V  ' 

9.989971 

1--I 

9498719 

8.306532n 

8.8702:'.n      91079891 

!i.!Mi:U02 

!i..">'.i:t730;i 

'ir.i/i 

9.596364 

9976 

1869 

-|»      -.:!i  1733/t 

8.870-J-JI       '.i;-i:no      '.i.iMKllOO 

:i.r.'.i:!7l-JH 

-.77S748n 

9.596369 

9.989978 

1883 

:n-      -.:in;-:.i;( 

8.870212     8.683940      '.I.'.M;:III:I- 

:i..v.i:;i;!i.|;i 

3.77805111 

9.598360 

:-.'-.' 

I  --!/>' 

-706 

BJU960H 

8.870203 

•-.-I      :i.!'.;:i(i'.i:. 

:'..7Kll!7.-.;i 

s.777353/1 

:>.:> 

9.969988 

1885 

T.OH 

8.870194 

8.687912       9.!K!3093 

9.593657N 

-.7;^ 

9.596354 

9469989 

I--,. 

8.331918* 

8.870185 

8.68H.-.I.-.      !>.:Mi:to:ii 

<.i.:.'.Kii;:i:i;i 

-.77.V.M:!« 

9J06354 

9.96)1 

I--7 

-700 

8.336800n 

8.870176 

8.691.-C.I      :i.'." 

!t.r.!l3t;-JlH 

S.77.V.>3C,/i 

9.596369 

9.969996 

!---/< 

8.34  !• 

8.870167 

0894 

9.988086 

S609H 

B.774599H 

9.596349 

9469996 

1—  i 

8.34643  In 

8.870158 

•771 

!i.:tt;:tn-i      :i..vi:t:.-i« 

B.773891JI 

9.696341 

9.969309 

-.:!.M  I7-/I 

-  -Tiil-1'.l 

'7717 

9.5935660 

B.773119H 

9.596346 

9.969306 

1891 

'-691 

8.355854n 

8.870140 

•.;.-,  i 

1060 

9.693648n 

3.779401fl 

9.696349 

9468809 

i  -  ••.•  /; 

8.360499n 

8.870130 

8.701577 

;I..YI:I.-,:«I;I 

3.77169011 

9.596340 

!l.!Ki2312 

•'17671       8.C7III-J] 

8.703493 

53076 

9.593519n 

8.77097711 

9.691 

9.989316 

18M 

BMfl      -.-71111-.' 

8.706409 

9.963079 

:i..v.»:i4!»4« 

3.770964fl 

9.596336 

9.969319 

i-  '-. 

-.n      -.-THICKS 

-.7117:111-,'     :i.:Mi:!ii7u     :(..v.i:u:t;»/ 

B.769549M 

9.596334 

9389 

i-  »./; 

-  JTOOOa      -.7(i:i|:M      !i.'.M;:!nr,7 

:>.:>:> 

8.768834fi 

9.606331 

9.969396 

1-  '7 

:  11077      !'.  • 

:i..v.i:u:;:.,, 

3.768116D 

16391 

9.969399 

i-  •- 

'In  .    -.-7nu;.-,      -.71  •.':!.-,:!      ;i. 

•I'.'lH 

B.7W 

9.596398 

9.969339 

I8M 

,.,      3.870066      -.7ii-r.t 

1060 

I403N 

-.:<:• 

9.596394 

9.988336 

-.-7ipn.-p<;      -.7i«;r.::i      '.i.'.»;:iii:,7      :I..Y':I.:-I/I 

8.76 

9.606391 

{339 

37 


TABLE  VI. 

CONSTANTS  FOR  THE  EQUATOR. 

Equator  and  mean  Equinox  at  the  beginning  of  the  Year. 

Year. 

# 

B< 

C< 

log  sin  a 

log  siu  b 

\ 

log  sin  r 

18565 

0    /   II 

90  48  50.1 

o   /   // 
2  38  7.2 

0    /   II 

350  59  24.5 

9.998801 

9.963607 

9.601800 

1857 

90  49  40.5 

2  38  57.1 

351  0  13.7 

9.998801 

9.9G3611      9.601782 

1858 

90  50  30.8 

2  39  47.0 

351   1   2.9 

9.!  198801 

9.963614 

9.601764 

1859 

90  51  21.2 

2  40  36.9 

351  1  52.2 

9.998801 

9.9636  is 

9.601746 

18605 

90  52  11.7 

2  41  27.0 

351  2  41.5 

9.998801 

9,963031 

9.601728 

1801 

90  53   2.0 

2  42  16.9 

351  3  30.7 

9.998801 

9.963625 

9.601710 

1869 

90  .->:!  52.4 

2  43  6.8 

351  4  19.0 

9.998801 

9.963628 

9.601692 

1863 

90  54  42.7 

2  43  56.7 

351  5  8.2 

9.998801 

9.963631 

9.601674 

18045 

90  55  33.2 

2  44  46.7 

351  5  58.6 

9.998801 

9.963634 

9.601657 

1865 

90  56  23.5 

2  45  36.6 

351  6  47.9 

9.998801 

9.963638 

9.601639 

1866 

90  57  13.9 

2  46  26.5 

351  7  37.2 

9.998801 

9.963641 

9.601621 

1867 

90  58  4.2 

2  47  16.4 

351  8  26.5 

9.998801 

9.963844 

9.601603 

18685 

90  58  54.7 

2  48  6.4 

351  9  15.9 

9.998801 

9.963647 

9.6015-.-, 

I860 

90  59  45.0 

2  48  56.3 

351  10  5.2    1    9.998801 

9.963661 

9.601567 

1870 

91   0  35.4 

2  49  46.2 

351  10  54.5 

9.998801 

9.963654 

9.601549 

J871 

91   1  25.7 

2  50  36.1 

351  11  43.8 

9.998802 

9.903057 

9.601531 

18725 

91  2  16.2 

2  51  26.1 

351  12  33.2 

9.998802 

9.963660 

9.601514 

1873 

91   3  6.5 

2  52  16.0 

351  13  22.5 

9.998802 

9.963664 

9.601496 

1874 

91  3  56.9 

2  53  5.9       351  14  11.9 

9.998802 

9.963667 

9.601478 

1875 

91   4  47.2 

2  53  55.8 

351  15  1.2 

9.998802 

9.963671 

9.601460 

18765 

91  5  37.7 

2  54  45.8 

351  15  50.6 

9.998802 

9.963674 

9.601442 

1877 

91   6  28.0 

2  55  35.7 

351  Mi  39.9 

9.998802 

9.963678 

9.601424 

1878 

91  7  18.4 

2  56  25.6 

351  17  29.3 

9.998802 

9.963681 

9.601406 

1879 

91   8  8.7  ' 

2  57  15.5 

351  18  18.6 

9.998802 

".963684       9.601388 

18805 

91  8  59.2 

2  58  5.5 

351  19  8.1 

9.998809 

9.963687 

9.601371 

1881 

91   9  49.5 

2  58  55.4 

351  19  57.5 

9.998802 

9.963691 

9.601353 

1882 

91  10  39.9 

2  59  45.3 

351  20  46.8 

9.998802 

9.963694 

9.601335 

1883 

91  11  30.2 

3  0  35.2 

351  21  36,2 

9.998802 

9.963697 

9.601317 

18845 

91  12  20.7 

3  1  25.2 

351  22  25.7 

9.998802 

9.963700      9.601299 

1885 

91  13  11.1 

3  2  15.1 

351  23  15.1 

9.998802 

0.903704      9.601261 

1886 

91  14  1.4 

3  3  5.0 

351  24  4.4 

!>.!«)8802 

9.963707 

9.601263 

1887 

91  14  51.8 

3  3  54.9 

351  24  53.8 

9.998803 

9.963710 

9.601946 

18885 

91  15  42.3 

3  4  44.9 

351  25  43.4 

9.998803 

9.963713 

9.60  1227 

1889  ' 

91  16  32.6 

3  5  34.8 

351  26  32.7 

9.998803 

9.963717       9.601209 

1890 

91  17  23.0 

3  6  24.7       351  27  22.1 

:  1.998803 

9.963720       9.601191 

1891 

91  18  13.3 

3  7  14.6       351  28  11.4 

9.998803 

9.963721       9.601173 

18925 

91  19  3.8 

3  8  4.6       351  29  0.9 

9.998803 

9.963727       9.601156 

1893 

91  19  54.2 

3  8  54.5      351  29  50.2 

9.998803 

9.963731       9.601138 

1894 

91  20  44.5 

3  9  44.4       35]  30  39.6 

9.998803 

9.903734       9.6011  20 

1895 

91  21  34.9 

3  10  34.3       351  31  28.0 

9.99---  (K! 

9.96373S       9.601102 

I896J9 

91  22  25.4 

3  11  24.3 

351  32  18.4       9.99.-S03 

9.963741 

9.601065 

1897 

91  23  J5.7 

3  12  14.2 

351  33  7.7       9.998803 

9.963745       9.601067 

1898 

91  24  6.1 

3  13  4.1       351  33  57.1       9.99SSD3 

9.90374*       9.601049 

1899 

91  24  56.4       3  13  54.0       351  34  10.4       9.998S03 

9.963751       9.601031 

190(1  5 

91  25  26.9       3  14  44.0       351  35  35> 

9.998803 

9.9637.54       9.601014 

H- 


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